I once had Châteubriand at John Q's restaurant, and I was wondering how to prepare this at home, and if it was filet mignon?

 We don't know how John Q's does it (or even whether John Q's does it anymore — Châteubriand is not currently listed on the Cleveland restaurant's menu), but this is how Elizabeth David does it, and that's good enough for us. (There is also another option, as well, in case Ms. David's recipe is just too brief).

For information on which cut of meat to buy, read What is Châteaubriand?.

Châteaubriand
From French Provincial Cooking, by Elizabeth David.

A châteaubriand steak is a cut from the centre and thickest part of the fillet, weighing about 12 oz., and enough for two people. It is too thick to be grilled on an ordinary domestic cooker, as the meat will be too near the flame and will dry up before it is sufficiently cooked. The best solution is, having painted the meat with olive oil and sprinkled it with a little coarsely-ground pepper, to give it about a minute on each side close to the hot grill and then to transfer it, standing on a rack in a baking tin to a very hot oven, Gas No. 8, 445°F (230°C), and roast it for about 12 to 15 minutes. Serve it with a sauce béarnaise.

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