Prepare steaks: Take 16 ounces filet mignon out of the refrigerator about an hour before you plan to cook them. Trim away any thick strip of fat. Coat both sides with 1 teaspoon kosher salt and 1/2 teaspoon pepper. Preheat oven to 400°F.
Heat the pan, then add everything: Heat an oven-safe stainless steel or cast iron pan over medium-high heat until it's really hot. Add 2 tablespoons butter, 2 cloves garlic, 2 sprigs fresh rosemary, 2 sprigs fresh thyme and the steaks all at the same time.
Sear steaks: Sear for 2-3 minutes on each side, constantly spooning the hot butter onto the steaks, and only turn them once after they get nicely browned. Keep the butter moving so it doesn't burn.
Finish in the oven: Transfer the pan to the oven. After about 5 minutes, start checking with an instant-read meat thermometer, beginning with the thinnest steak. Remove each steak when it reaches 115-120°F for rare, 125-130°F for medium rare or 130-135°F for medium. 2-inch steaks usually take 5 to 10 minutes. Rest on a plate, loosely tented with foil, for 5 minutes (temperature should rise another 5 degrees).
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Notes
I can't stress enough how important it is to let your steaks come to room temperature. They're thick cut, and if they're super cold in the middle, you risk overcooking the outside before the middle is done. Take them out about an hour ahead, but no longer than 2 hours (1 hour if your kitchen is above 90°F).
Optional infused butter: for even more flavor, warm the butter, garlic and herbs over the lowest heat for an hour or more before cooking, burner on the whole time. When you're ready, pour the butter into a bowl, remove the garlic and herbs (they make a great garnish), heat the pan over medium-high until really hot, add the steaks and spoon the butter back in.
The steaks cool the pan just enough to keep the butter from burning. Keep it moving with your spoon.
Steaks of different sizes won't finish at the same time. Check the smallest one first and pull each one as soon as it's done.
If you accidentally take one too far, get it out of the hot pan right away to rest on a plate. Resting in the pan keeps cooking it.
The best type of pan is either cast iron or a high quality stainless steel. Just be sure it is oven safe.