In a mixing bowl, combine hamburger meat with finely chopped onion, fresh basil, teriyaki sauce, bread crumbs, and parmesan cheese. Use your hands or a spatula to ensure even mixing, but be cautious not to overwork the meat.

Mix until well combined and form into patties, aiming for uniform thickness of about ¾ inch for even cooking.

Preheat your grill to medium-high heat (around 375°F).

Grill the patties for about 5-6 minutes on each side, or until each reaches your desired doneness. Look for juices bubbling at the edges and a beautifully seared crust to indicate readiness.

Serve on buns with your choice of toppings, such as lettuce, tomato, pickles, or additional parmesan for a gourmet touch.