Step 1

Prepare a charcoal or gas grill for medium heat. (Medium is 325 degrees to 375 degrees. You should be able to hold your hand 4 to 5 inches above the grates for 6 to 7 seconds.)

Step 2

Thinly spread mayonnaise on one side of each piece of bread. When you're ready to grill, take the bread, cheese, salt and a spatula to the grill. Clean the grates with a grill brush. (No need to grease the grates.) Place the slices mayonnaise side down on the grill. Evenly sprinkle half the slices with about 3/4 cup cheese. Cover the grill and cook until the bread is golden and the cheese is nearly all melted, 4 to 6 minutes. Check on the bread often, moving slices around the grill as needed to avoid burning.

Step 3

Use the spatula or your hands to top the cheese halves with the other toasted slices. Transfer to plates, press down slightly and sprinkle with salt.