If making on the stove, start by preheating a cast iron skillet until smoking. If grilling outside, prepare a charcoal grill.
Butter the buns and grill, cut side down, for about 1 minute or until toasted. Reserve.
Season the burger patties with salt and pepper.
If using the cast iron, lightly grease with some olive oil. Cook the patties for about 4 minutes, flip and add 1/4 of the blue cheese per burger. Cover with a lid and cook for 3 more minutes for medium-rare. Allow the burgers to rest for 5 minutes.
Add 1 tablespoon of mayo to the buns. Place the burgers in each bun and finish with some lettuce and tomato.