Pat the filet mignon steaks completely dry with paper towels. This is crucial for achieving a good sear. Season generously on all sides with salt and freshly ground black pepper.
Heat the olive oil in a heavy-bottomed skillet (cast iron works best) over medium-high heat until it shimmers but does not smoke.
Carefully place the seasoned steaks into the hot skillet. Sear for 2-3 minutes per side, until a deep brown crust forms. Do not move the steaks around while searing.
Reduce the heat to medium. Add the butter, smashed garlic cloves, and herb sprigs to the skillet. As the butter melts, tilt the pan and use a spoon to baste the steaks with the melted butter, garlic, and herb mixture for about 2-4 minutes, or until your desired level of doneness is reached. For medium-rare, aim for an internal temperature of 130-135°F (54-57°C).
Remove the steaks from the skillet and place them on a clean cutting board or plate. Let them rest for at least 5-10 minutes before slicing or serving. This allows the juices to redistribute throughout the steak, ensuring maximum tenderness and flavor.