There are many options where the meat can be cooked well without sacrificing quality. We would suggest that you make some type of pot roast or stew. Boeuf Bourguignon, Coq au Vin, Blanquette de Veau, Lamb Stew, Veal Marengo are all options.
Or you could pan fry or grill steaks to order, or grill chicken breasts, or stir-fry something. If this person is so particular, cooking the piece separately, well done, would do it - a little more work for you, though.