Shape ground beef into eight patties, approximately 4 1/2-inch diameter.
Place approximately 1/4 cup of cheese mixture in center of four patties; top with remaining patties. Press edges firmly together to seal; gently pat to 3/4-inch thickness.
In small bowl, combine Italian seasoning, garlic powder, and pepper. Press evenly into both sides of each patty.
Place patties on grill over medium, ash-covered coals. Grill, uncovered, 22 to 24 minutes to medium doneness (160 degrees) or until centers of patties are no longer pink and juices show no pink color; turn occasionally.
Season burgers with salt, as desired. Line bottom of each roll with one tomato slice; top with burger.