Preheat oven to 350°F.
Place a large skillet over medium-high heat, add 3 tablespoons EVOO. Add the red and green bell peppers and onions, season with salt and pepper, and cook for about 6-8 minutes. Sprinkle the pepper mixture with some flour and stir to combine. Add balsamic vinegar and cook an additional 1-2 minutes. Set aside and keep warm.
While the pepper and onion mixture is cooking, place a medium-size skillet over medium-high heat and add remaining tablespoon of EVOO. Cook sausages about 4 minutes per side or until brown, crispy and cooked through.
Place the hot dog buns on a baking sheet, top one half with a slice of cheese and toast. Place a sausage on the bun and top with the pepper and onion mixture.