Heat olive oil in a pan or skillet, then add sliced bell pepper and onion. Cook on medium to high heat and stir occasionally until the peppers and onions are soft, roughly 5-8 minutes. Remove vegetables from the pan and set aside.
Cut 4 slices of bologna about half an inch thick. Set the bologna in the skillet on medium heat. Cook each side for 2 minutes. While the second side is cooking, add a slice of cheese to the top of each piece of bologna.
Cut the rolls and add mustard or another condiment of your choice to the bun before placing the cooked bologna with cheese on the bun.
Top the bologna with the onions and bell peppers. Close the sandwiches and serve.