Combine, hamburger salt and pepper in a large bowl. In another bowl, combine the coarsely shredded sharp cheddar and pepperonis. Let bacon and cheese mixture sit at room temperature for about 20 minutes to get soft. Then, shape mixture into balls (for however many burgers you would like to make).
Form 2 patties of meat and place one cheese/pepperonis balls in between them. Pinch the sides together to seal in cheese ball. Gently press formed patty, to spread out cheese ball. Continue until all patties are formed.
Cook burgers on grill over medium flame for about 7 minutes on each side.
While burgers are grilling, flip burgers, and baste the cooked side of the patties with the pizza sauce After about 7 minutes longer, the burger should be done (these are big thick burgers and may take longer to grill to your liking). Baste again with the pizza sauce before removing from grill. Butter hamburger buns and place on top rack of grill for several minutes, until toasted.
To build burger, take toasted bun, add patty, you can add tomato or lettuce, if you would like, but the flavors are great without them.