Bring the meat to room temperature and season both sides with salt and pepper.

Preheat the oven to 425°F.

Heat the olive oil in an ovenproof stainless-steel or cast-iron sauté pan on the stovetop over medium-high heat for a few minutes, until the oil gets very hot to the point where you begin to see slight wisps of smoke. Add the filets and brown them on one side for exactly 4 minutes.

With tongs, flip the steaks over and immediately place the pan in the preheated oven. Cook the steaks for another 6 minutes for medium rare.

Using an ovenproof glove, carefully remove the pan from the oven and, with tongs, transfer the filets to a clean plate. Cover them tightly with heavy-duty aluminum foil and leave them to rest for 5 minutes. Then, serve them immediately, topping each with 1 tablespoon of butter, spooning the hot juices over the butter to melt it.