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Step 1
Liberally season steaks on both sides with plenty of salt, as well as fresh cracked black pepper to taste. Place on a wire rack over a baking sheet and let sit at room temperature for at least 30 minutes, preferably a couple hours. If letting stand for more than one hour, keep in refrigerator, then let stand at room temperature 30 minutes before cooking.
Step 2
Meanwhile, make garlic herb compound butter: place all ingredients in a food processor and process until smooth. Spoon onto a piece of plastic wrap and roll into a log shape. Chill until firm.
Step 3
Preheat the oven to 250º F. Place the pan with steaks in the oven and insert an internal meat thermometer with probe. For medium rare, cook until the internal temperature reaches 120º Fahrenheit, about 25-30 minutes. Larger or thicker steaks will take longer; I highly recommend using an internal meat thermometer with probe here. To cook filet mignon steaks to a different warmth, like medium or medium well, see note.
Step 4
Remove from oven when internal temperature reaches 120º F. Preheat a cast-iron skillet over high heat for 5 minutes while steaks rest. Pat steaks dry.
Step 5
Carefully place steaks in hot skillet and cook 45 seconds; flip and place a pat of garlic herb compound butter, about 1 tablespoon per steak, on top of the filet. Cook another 45 seconds, then flip a couple times until steaks are a richer brown color, about 20-40 seconds total. Press the sides of the filet up against the sides of the cast iron skillet briefly until no longer red or pink. Remove from skillet and serve with more garlic herb compound butter.