Wrap the grated zucchini in a clean dish towel. Twist the towel tightly (over the sink or a bowl) to wring out the excess moisture from the zucchini.
Add the zucchini to a mixing bowl along with the beef, egg, Parmesan cheese, basil, parsley, breadcrumbs, garlic, oregano, salt, and pepper. Using your hands, mix gently just until all of the ingredients are combined. (Avoid overmixing to keep the burgers as tender as possible.)
Pre-heat a charcoal or gas grill (or grill pan, or cast iron skillet) over medium-high heat.
With damp hands, mold the meat into four ¾-inch thick patties. (The patties will be quite large.) Make a small indent with your thumb in the center of each burger to keep it from puffing up on the grill.
Place the burgers on the hot grill, thumbprint side down, and cook for 4 minutes (with the grill lid up). Flip the burgers over and immediately top each patty with ¼ cup of Rao’s Homemade Arrabbiata Sauce and 2 thin rounds of mozzarella. Put the grill lid down and cook for 4 to 5 minutes until the cheese is melted and the burgers are cooked to medium (aka slightly pink in the center). Remove the burgers from the grill and tent loosely with foil. Rest the burgers for 5 minutes to allow the juices to redistribute.
Meanwhile, grill the buns if you’d like. Brush the cut sides of each bun with a tiny bit of olive oil. Place the buns, cut side down, on the grill for about 1 minute or until grill marks appear.
Serve the burgers warm on the toasted buns garnished with extra basil leaves and/or crushed red pepper if you’d like. Feel free to serve with extra warmed Arrabbiata Sauce for dipping.