Heat 2 tablespoons oil in skillet over medium heat. Add the bell pepper, onion, and ¼ teaspoon salt. Cook until softened, 7 to 8 minutes.
Meanwhile, heat grill to medium-high. In a large bowl, combine pork, sausage, ¼ teaspoon salt, and 1/8 teaspoon pepper. Form 4 patties, each about ¾ inch thick.
Grill patties until cooked through, 6 to 7 minutes per side. (Or heat 2 tablespoons oil in grill pan over medium heat and cook patties, 7 to 8 minutes per side.)
Place burgers on rolls with onions and peppers. Add ketchup, if desired.