1In large bowl, mix beef, Italian seasoning, salt and pepper. Shape mixture into 8 patties, 4 1/2 inches in diameter and 1/4 inch thick. Press 1/4 cup of the cheese into a ball with hands; press flat into 3 1/2-inch-diameter patty. Repeat with remaining cheese. Place cheese patties on top of 4 beef patties; top with remaining beef patties. Pinch edges together to seal.
2In 10-inch skillet, heat oil over medium-high heat. Add mushrooms; cook 4 minutes, stirring occasionally, until lightly browned. Add garlic; cook 1 minute longer. Remove from heat.
3Heat gas or charcoal grill. Place patties on grill over medium heat. Cover grill; cook 11 to 13 minutes, turning once, until meat thermometer inserted in center of patties reads 160°F. During last 2 minutes of cooking, place buns, cut sides down, on grill until toasted.
4Place burgers on bottom halves of buns. Top with pizza sauce and mushroom mixture. Cover with top halves of buns.