How to Broil or Bake Filet Mignon. 1  For cuts that are less than 1-1/2 inches thick, position the broiler rack so the steak will be 3 to 4 inches from the heat. 2  For cuts that are 1-1/2 inches thick, position the broiler rack so the steak will be 4 to 5 inches from the heat.3  Preheat the broiler. Place the filet on the grill rack over the heat. 2  Cover the grill. 3  Use the following timings for grilling filet mignon, and turn once halfway through the grilling time: 4  For a 1-inch cut, grill 10 to 12 minutes for medium rare (145 degrees F) or 12 to 15 minutes for medium (160 degrees F).