In a large mixing bowl combine 1/2 cup of the shredded mozzarella with the Worcestershire sauce, garlic salt, black pepper, dried onion flakes, and oregano.
Add the ground beef to the seasoned cheese mixture and mix gently until just combined; avoid overworking the meat.
Divide the mixture into four equal portions and shape each into a patty about 1/2 inch thick.
Preheat grill or grill pan to medium heat. Grill the patties 4–5 minutes per side, or until an instant-read thermometer inserted into the center reads 160°F (71°C).
Sprinkle the remaining shredded mozzarella over the patties, cover, and grill 1–2 minutes more until the cheese is melted.
Remove the burgers from the grill. Butter the insides of the buns and place them butter-side down on the grill until lightly golden.
Assemble the burgers by placing each patty on a bun, spooning about 2 tablespoons marinara sauce over each (adjust to taste), and topping with the bun tops.
Serve immediately with desired accompaniments.