Shape beef into desired number of uniform patties. If using two patties per burger, press to approximately ¼-inch thickness. Season with salt and pepper.
Preheat gas or charcoal grill to 400°F. Place burgers on oiled grates and grill until desired internal temperature, turning once. Top with cheese. Brush butter on buns and grill until browned.
Remove from grill and place on bottom half of bun. Assemble with desired toppings.