Step 1Trim the meat of any thick layers of fat, leaving the thin streaks in place. These will melt as the meat cooks and be a vehicle for the pepper flavor. Leave the delicious, streaky "rope" of muscle that runs the length of the fillet attached, however tenuously, to the roast, but check for and remove large lumps of fat it might conceal.
Step 2Concerning the satiny "silver skin" that sheaths one face of the fillet: Where it is thin, soft and translucent, leave it intact. You won't notice this tender sinew once the meat is cooked. Where it is opaque and tough, near the fat end of the fillet, slide the tip of your knife just beneath the surface to remove a few thick strips of it. But don't bother being meticulous.
Step 3Season the trimmed fillet moderately overall with salt, sprinkling more heavily on the thick sections. We use a scant three-fourths teaspoon sea salt per pound of meat. Next roll the fillet in freshly, coarsely cracked black pepper. We use about 1 teaspoon per pound. To ensure even cooking, truss the fillet, one string every few inches. Cover loosely and refrigerate for 1 to 2 days.
Step 4About an hour before serving, heat the oven to 400 degrees or light a charcoal fire and remove the fillet from the refrigerator.
Step 5Sear on a hot grill or griddle, under a very hot broiler or, if somewhat awkwardly, curled in your largest skillet. For reference, take the temperature at the centers of both the thick and the thin ends of the fillet -- they should be between 60 and 70 degrees. The meat will feel soft and limp. You can hold it for up to an hour this way before cooking.
Step 6To cook, place the seared fillet on a heavy, rimmed sheet pan in the oven or back on the grill over medium coals. If grilling, plan to turn the meat every 10 minutes or so. Whether roasting or grilling, start checking the doneness after 15 minutes. Check both ends. For a very rare fillet, remove the fillet from the heat when the center of the thick end registers 105 degrees (it will feel only barely firmer than before). For a very rosy medium rare, remove from the heat at about 115 degrees. For "just a little pink," cook to 125 degrees. At this point the tender muscle will begin to feel "flexed" firm. Cooking time will depend on the heat source and the thickness of the meat. A skinny fillet that was over 70 degrees to begin with may be very rare in less than 20 minutes.
Step 7If roasting a whole fillet, remember that the skinny end will cook faster, running about 10 degrees hotter than the fat end. This is convenient, if you want to offer a range of doneness. If you want the whole roast to emerge the same doneness, loosely wrap the skinny end with foil, shiny side out, when it tests about 95 degrees.
Step 8In any case, loosely tented, in a warm spot, the meat will continue cooking after you remove it from direct heat. Expect the temperature to increase about 10 degrees in 10 minutes. Although tenderness is not an issue with fillet, I think it has the best flavor if allowed to rest 10 to 15 minutes.
Step 9Because fillet is very tender, you can carve it as thinly or thickly as you like, but respect the mostly regular grain of the muscle. Don't remove the trussing strings on any part of the fillet that you don't intend to carve right away.