Preheat oven to 410F.
To make the compound butter, take the butter out of the fridge and let it sit at room temperature while preparing herbs and garlic. In the meantime, rinse rosemary, parsley and oregano, chop and set aside. Blanche garlic, if needed, by bringing 1 cup of water to a boil in a small saucepan, taking the water off the heat and letting the garlic blanch in hot water for 1 minute, then cooling in cold water. If the butter is too hard, microwave for 10 seconds or pound by a pasta roller.
Add the chopped herbs and minced garlic, and mix in until evenly distributed. Shape into a log and refrigerate until ready to use. Remove the butter from the fridge 10 minutes prior to using.
Remove filet mignon steaks from the fridge about 45-60 minutes before cooking and let come up to room temperature. Liberally season with salt and pepper on both sides just before searing. See Note.
Heat the olive oil and the butter in a large (12") cast iron pan over medium-high heat. When the butter starts smoking and turns dark brown in color, place the filets in the pan and sear undisturbed for about 2 minutes. Flip and sear for another 2 minutes. Flip the steaks again and immediately transfer the pan into the preheated oven.
Bake to desired doneness: rare - 120F-125F, medium rare - 130F-135F, medium - 140F-145F, medium well - 150F-155F and well done - 160F-165F.
Remove the filets from the skillet and place on a platter. Cover with foil and let the steaks rest for 3 minutes. Top with a slice of compound butter and serve immediately.