Hold the pepper upright on a cutting board by the stem. Cut straight down the side of the pepper with a sharp knife taking off the entire side in one slice. Cut off the remaining three sides so that you have four fairly large, flat pieces of pepper. Drizzle the peppers with olive oil and sprinkle with salt and pepper.
Put the slices skin side down on a medium hot grill, turning when the peppers look soft and slightly charred.
Fit a slice of cheese into the pepper and leave on the grill until the cheese melts.
Serve 2 pieces on each bun and top with dilled Mayonnaise