White-meat turkey is lower in calories and fat than traditional burgers, but when you top this version with melted Swiss cheese, roasted red peppers, arugula, and grilled red onions, you'll hardly miss the beef.
Finely chop enough onion to yield 1/3 cup (reserve remaining rounds for burgers). In a large skillet, heat oil over medium-high; cook chopped onion and mushrooms, stirring occasionally, until onion is soft and mushrooms are golden, about 4 minutes. Season with salt and pepper, then transfer to a cutting board and roughly chop mixture.
Heat a grill to medium-high. Clean and lightly oil hot grill. Season onion rounds with salt and pepper; grill until lightly charred and tender, 5 minutes, flipping once. In a large bowl, combine mushroom mixture, turkey, and parsley. Form into four 1/2-inch-thick patties; season with salt and pepper. Grill, about 4 minutes, flipping once. Top each patty with cheese; grill until burgers are cooked through and cheese is just melted, 1 minute. Serve burgers on buns with grilled onions, peppers, and arugula.