Place a large skillet over medium-high heat with 2 turns of the pan of EVOO, about 2 tablespoons. Add the onion, peppers, and garlic to the pan and cook until the veggies are tender, 7-8 minutes. When the veggies are tender, add the Worcestershire and season with salt and pepper.
While the veggies are cooking, place a second skillet over medium-high heat with 1 turn of the pan of EVOO, about 1 tablespoon. Shape the sausage into thin patties and wrap the meat around the cubed cheese. Cook patties 4 minutes on each side until deep brown and firm.
Place patties on roll bottoms and top with peppers and onions. Set roll tops in place and serve.