1In small bowl, mix Garlic Parmesan Aioli ingredients; cover and refrigerate. Heat gas or charcoal grill. In medium bowl, mix beef, bread crumbs, milk, salt, pepper and onion. Shape mixture into 4 patties, about 1/2 inch thick. Make indentation the size of a quarter in center of each burger so burgers remain level during grilling.
2Place patties on grill over medium heat. Cover grill; cook 10 to 12 minutes, turning once, until meat thermometer inserted in center of patties reads 160°F. Toss green and red bell pepper rings with oil to coat. Add bell pepper rings to side of grill for last 8 to 10 minutes of cooking, turning once, until crisp-tender. During last 2 minutes of cooking, top each patty with cheese. Cook until cheese is melted.
3Spread about 1 tablespoon Garlic Parmesan Aioli mixture on cut sides of buns. Place burgers on bottom halves of buns; top with peppers. Cover with top halves of buns.