Preheat a grill to medium. Heat the olive oil in a large skillet over medium-high heat. Add the bell peppers and onion and season with a pinch each of salt and pepper. Cook, stirring frequently, until lightly browned and just tender, 8 to 10 minutes. Add the garlic and cook until just softened, about 1 more minute. Stir in the pizza sauce and 1/2 cup water and simmer until thickened but still saucy, about 5 minutes. Set aside and keep warm.
Combine the beef, sausage, sage, oregano and 1 teaspoon each salt and pepper in a large bowl. Mix with your hands until well combined. Form into six 1-inch thick patties (about 4 1/2 inches wide). Season the patties with salt and pepper.
Grill the burgers until cooked through, 6 to 7 minutes per side; top each with a slice of cheese during the last 1 to 2 minutes and cover to melt. Served the burgers on the buns and top with the peppers, onion and basil.
