Fillet steak, also known as filet mignon and tenderloin steak, is one of the leanest cuts of beef available, known for its soft texture and very little fat. It's taken from the small end of the tenderloin. Before cooking fillet steak in a hot oven, season it well and sear it in a hot pan. That way you'll lock in the flavor of the steak with a nice thin char. Once it's in the oven, use a meat thermometer to avoid overcooking.
Preheat the oven to 450 degrees Fahrenheit.
Season the steak with salt, pepper and other seasonings you like. Then, sear it on the stove over medium-high heat in an oven safe frying pan or skillet. Cook for 30 seconds per side for every inch of thickness, using tongs to flip the steak. Use a cooking oil with a low smoke point -- safflower or coconut, for example.
Insert the oven safe meat thermometer halfway into the middle of the steak.
Transfer the pan to the preheated oven. Cook until the steak reaches the desired internal temperature: 120 F (very rare), 140 F (rare), 145 F (medium rare), 160 F (medium) or 170 F (well). Thicker steaks (1.5 to 2 inches) continue cooking when resting, so if you're using thick fillet steak, remove it when it reaches a few degrees below these temperatures.
Place the steak on a plate or cutting board to rest for 5 to 10 minutes. Thicker steaks should rest closer to the 10-minute mark.