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Step 1
Preheat the oven to 400°F (200°C). Remove the steaks from the fridge and let them come to room temperature (about 30 to 40 minutes before cooking). Season all sides of the steaks with salt and pepper.
Step 2
Heat an empty oven-safe pan (I recommend cast iron) on the stove over high heat. Once the pan is very hot add the oil. Once the oil shimmers in the pan (i.e it's sizzling hot), sear the steaks for 2 minutes, until they have a nice golden crust. Roll them on their sides for another 1 minute to get a crust on the edges. Lastly, flip them onto their final side and while the steak is searing, add the butter, garlic, and rosemary to the pan. Butter baste the steaks with a spoon for 1 minute (watch the video above to see how I do this).
Step 3
Transfer the hot pan to the oven (make sure to use oven mitts with cast iron) and bake for an additional 4 to 10 minutes, depending on the desired level of doneness (see chart above). My personal favorite is removing the steaks from the oven at 120°F for medium rare.
Step 4
Remove the cooked filet mignon steaks to a plate, cover them with aluminum foil, and let them rest for 5 to 7 minutes before serving. The resting period will ensure your steaks are cooked through to the proper serving temperature.
Step 5
Top with hot melted herb butter from the pan (alternatively, you could add a fresh slice of compound butter) or a drizzle of bearnaise sauce before serving.