She emerges 10 minutes later, her face suffused with a deathly pallor. How did it go? "Oh, fine," she says through clenched teeth, struggling to compose her features into a mask of wounded stoicism, "just fine."
He who laughs first lives to think better of it. It transpires that the problem with the Penn interview experience runs rather deeper than the man's dietary requirements.
Having painstakingly constructed an image of himself as a distinctive and potentially entertaining individual - putting a murky brat-pack past behind him to mature into a fine character actor; shaking off the "Sean's brother" tag to make his mark as a Reservoir Dog; and pulling off a neat star turn in Robert Altman's excellent Short Cuts - Penn is now hell- bent on exploding Hollywood's cult of personality. And if he has to pose as a large slab of granite to do it, that sacrifice will not be beyond him.
Anyone who saw the articulate and amusing person who made such a splash on Carlton TV's hilarious Hollywood Men poised pugnaciously on an LA barstool, being genially satirical at the expense of his fellow film industry professionals, would not recognise the Penn of this particular Tuesday lunchtime.
He lounges, bulkily be-denimed, behind the ravaged remains of his huge repast. As a gold belt which Garth Brooks might discard on the grounds that it was insufficiently cosmopolitan strains to contain his burgeoning girth, Penn's response to introductory pleasantries blurs the line between yawn and scowl.
Polite inquiries as to the state of his health - an enthusiastic and once semi-professional kick-boxer, Penn had hurt his back sparring in an East London gym the day before - are met with a curt "I'm all right, get off that."
Stomach beginning to knot with anxiety, his interviewer struggles to head off an awkward silence with a stock question about the beginnings of Penn's film career: whether he had felt any resistance to the idea of joining what is in effect (father Leo a director, mother an actress, brother the star of Shanghai Surprise) the family business. "I think it was always apparent that I would eventually become involved," Penn asserts flatly, "because I wanted to."
What about the boxing, though? Did that ever look like it might become a career? "Boxing's not a career for anyone: it doesn't last long enough to be a career." But most people who do it don't have an alternative. It's probably their best chance of making some money, so if someone with plenty of other options got into the ring, they would presumably have to have other reasons for doing so, wouldn't they?
A long pause. "Yes." The silence multiplies geometrically rather than arithmetically. "I suppose" - another long pause fosters the cruel illusion that something interesting is going to be said - "I liked it."
At this stage, it would be fair to say that things are not going well. The only way forward seems to be to go for the direct approach and appeal to the subject's better nature. Without wishing to imply that he has been resistant in any way, is there anything Penn might enjoy talking about? "Go ahead. Just keep asking questions." But you're just going to keep on saying "yes" and "I liked it". Can't you imagine what that is doing to my fragile self-esteem?
Somewhere within the derelict mineshaft of Penn's personality, a cigarette lighter of humanity flickers. "Well, I suppose if you want to know why I fight, it's because when I was a kid in LA I played football, and when I got to high school the particular school I was at had a very good football team. I didn't make it into the first string and I didn't like being second string, so I started wrestling and got on the team for that. School ended abruptly for me - they wanted me to leave and I wanted to leave too, so it was mutual - and there wasn't any way of wrestling any more, so I went to a boxing gym and got into that, and then I started kick-boxing and found out I was pretty good at it, and from the ages of about 20 to 27 that was what I spent a fair amount of my time doing."
It's rather a rude question to ask but people always seem to want to know: would he mind telling us how old he is now? "I'm getting up there ... I've stopped saying."
This statement is made very firmly and with no trace of humour. It would be a shame to let the newly conducive atmosphere founder on something so trivial as a date of birth. Oddly enough, Penn seems to find questions about his five-year cocaine addiction much less intrusive.
Did he make a conscious decision to make a mess of things? "No, it happened gradually. I started to play around with it a little bit and then I had a tragedy happen. I lost a daughter - she was only two days old, she was born premature and her lungs were just too weak - and I went kind of overboard.
"I just used it as an excuse to do as many drugs as I could. It took me a year or so to figure out what I was doing and by then I was completely addicted."
Does he understand now what made him do it? "I don't think it was insecurity or anything like that. I just genuinely liked the physical high. I can remember when I was a little kid going on a swing and spinning in circles upside down ..."
At this point, Penn is called to the phone to speak to his girlfriend. On returning, he is impressed to find out that I know she is a model called Stefianna Dela Cruz, also known professionally as the "Asian Budweiser girl".
Is it a source of great pride to him to be involved with a high-profile object of beauty? "I wouldn't care if she was a f---ing plumber. She started modelling after we got together, not before, and she was always beautiful. I don't need a campaign or an agency to tell me that."
All of a sudden, we seem to be the best of friends. Unfortunately, the over-confidence which results from this sudden camaraderie prompts the kind of broad conceptual question that would probably have been better unasked. Penn's new film, Mulholland Falls, is a strange piece of work: it starts out as a straightforward elegiac LA cop drama in the Chinatown mould and then turns into a bizarre nuclear allegory. But it still seems to nestle securely in the "group of guys" tradition.
Does Penn think this genre - from The Magnificent Seven to Reservoir Dogs - tells us something vital and intimate about male relationships?
"I think people [ie you, you effete English scumsucker] tend to over- intellectualise these things. The bottom line is that groups of guys have been hanging out together since the beginning of time. It's not a genre, it's just another subject."
Perhaps sensing that things have gone awry again, Penn's make-up woman makes a demure entrance. She is here to cover up the scratches on his right cheek, caused by the laces on the boxing gloves of his last sparring partner. When her work is done, he inspects her handiwork in a small compact mirror and pronounces himself ready for the photographer.
Does this scratching thing happen often? "It's very rare. It only comes about when a guy's getting his ass kicked and trying every trick in the book." Is there something bracing about the pain of laces cutting into your cheek?
Realising that the pressure of the moment has caused him to say something completely insane, the person who asked this question is glad when it is answered with silence.
Does it matter if there are marks on a film star's visage? The thinnest trace of a smile plays across Chris Penn's lips: "Not with my face it doesn't."
8 'Mulholland Falls' opens next month.