In a bowl, gently mix the ground beef with salt and pepper. Divide the beef into 4 equal portions and form them into burger patties.
Preheat your grill or a skillet to medium-high heat.
Grill or cook the burger patties for about 4-5 minutes per side, or until they reach your desired level of doneness.
During the last minute of cooking, spread pizza sauce on the top half of each burger bun. Top the cooked patties with mozzarella cheese, pepperoni, olives, and bell pepper. Cover the grill or skillet for a minute to melt the cheese.
Assemble the pizza burgers by placing the topped patties on the bottom halves of the burger buns. Serve immediately.