Combine the 1 cup butter, blue cheese, 1 1/2 teaspoons salt and 1/2 teaspoon pepper in a food processor. Process until well blended and smooth. Transfer to a sheet of plastic wrap and roll into a cylinder. Wrap tightly and place in the freezer to chill.
Remove the steaks from the refrigerator and let them come to room temp for 30 to 45 minutes. Meanwhile, preheat the oven to 450 degrees F.
Sprinkle the steaks with salt. Heat a cast-iron grill pan over high heat until starting to smoke, then add a small amount of oil to the pan. Place the steaks in the pan and cook for 4 minutes. Flip and cook for another 4 minutes. Turn off the oven and transfer the pan to the oven for 8 minutes, or until the steaks reach an internal temperature of 155 degrees F.
Place 1/2 tablespoon of the remaining butter on each steak and allow the steaks to rest for 5 minutes before serving; the internal temperature will climb another 5 degrees.
Serve the steaks topped with blue cheese compound butter.