Take your steaks out of the fridge and let them get closer to room temperature while you put together your butter mixture.And for that butter mixture cut the butter into pads and put the pads on your cutting board. Mince the garlic, zest the lemon and chop the parsley.Put the parsley, garlic, lemon zest, dried basil, grated parmesan and cayenne pepper on top of the butter and using a table knife or a small spatula mix it all together and form it into a kinda mini loaf of bread shape.
Put skillet on at medium high and swirl in just about a tablespoon of olive oil and plunk in a tablespoon of the butter mixture. While the skillet is getting hot generously salt and pepper both sides of the filets. When the oil and butter have stopped acting up and leveled out put in the steaks. The butter and oil will foam up again but that's ok. Cook the steaks about 3 minutes a side and test them. When the steaks are just starting to get firm or they read 130° on an instant read meat thermometer they are rare. When they are definitely firm to a poke and read 165° they are well done. The in-betweens will give you medium rare, medium and medium well. I'm sure that your meat thermometer has the temperatures listed on it or they came with it on paper.
Serve up your Filet Mignon steaks and top with the butter mixture and the liquid from the skillet.