Preheat the oven to 425°. In a deep skillet, arrange the sausages in a single layer, add about 1/2 inch of water and 1 tablespoon EVOO, 1 turn of the pan, and bring to a boil over medium-high heat. Cook until the liquid evaporates and the sausages are browned, about 20 minutes. Set aside.
While the sausages cook, in a large soup pot, heat the remaining 3 tablespoons EVOO, 3 turns of the pan, over medium-high heat. Add the potatoes, Cubanelle peppers, bell peppers and onion, season with salt and pepper and cook until the vegetables are slightly softened, about 5 minutes. Stir in the chicken broth and tomatoes and bring to a simmer, scraping up any browned bits from the bottom of the pan. Lower the heat to medium-low and cook until the vegetables are tender, about 12 minutes.
Meanwhile, combine the basil, cheese, butter, sun-dried tomato paste and garlic. Spread the basil butter on the bread and cut into large bite-size cubes. Place on a baking sheet and bake until crisp, about 5 minutes.
Slice the reserved chicken sausages, divide among 6 soup bowls, cover with the stoup and top with a few Gobble-'Ems. Pass the cheese around the table.