For the Chunky Pizza Sauce, heat the oil in a medium saucepan over medium heat. Add the garlic and cook 1 minute, stirring constantly. Add the canned tomatoes, tomato paste, Italian herb seasoning, sugar, salt, and black pepper, and cook until thickened, about 5 minutes, stirring frequently and using a wooden spoon to break up the tomato pieces a bit. Set aside.
For the Pizza Burgers, use your hands to combine the ground beef, grated onion, steak seasoning, Worcestershire sauce, coconut aminos, and Italian herb seasoning in a large bowl; be careful not to over-mix the meat. Divide the meat into 4 equal portions and shape each into a patty.
Grill the burgers over medium-high heat until done (hamburger meat should be cooked until it’s no longer pink in the center), about 4 to 5 minutes per side. When the burgers have about 2 minutes left to cook on the second side, spoon about 3 tablespoons of Chunky Pizza Sauce on top of each, and then top each with 1 oz of cheese. Cover the grill (or tent a piece of foil over the burgers) so the cheese melts.
Transfer the burgers onto the buns and sprinkle the parsley on top of the cheese; serve the burgers along with the rest of the Chunky Pizza Sauce for dipping.