Remove filet mignon from the refrigerator. Salt all sides generously and allow them to sit at room temperature for 45 minutes
Preheat the oven to 400 degrees
Add butter to a cast-iron skillet and heat to medium-high until butter is fully melted
Season filets with pepper before placing them in the pan. Sear for 2-3 minutes until golden-brown crust forms. Flip to the other side using tongs and sear for another 2-3 minutes
Turn off the stove and move the skillet to the oven's middle rack. Continue cooking for 5-6 minutes in the oven for medium-rare, or leave in for another minute or two for medium doneness
Place steaks on a cutting board or plate tented with foil for 5-10 minutes to rest before serving