Heat broiler. Heat the oil in a large skillet over medium heat.
Add the onion, ½ teaspoon salt, and ¼ teaspoon pepper and cook, stirring occasionally, until the onion begins to soften, 5 to 6 minutes.
Add the bell pepper and cook, stirring occasionally, until softened, 5 to 6 minutes.
Add the spinach and cook, tossing, until the spinach is just wilted, 1 to 2 minutes.
Meanwhile, remove the sausage from their casings and form into twelve ½-inch-thick patties. Place them on a broilerproof rimmed baking sheet and broil until cooked through, 4 to 5 minutes per side.
Form sandwiches with the rolls, sausage patties, and vegetable mixture.