Preheat the oven to 350°. Place the peppers on a baking sheet and roast them for 60 minutes.
Peel the peppers, and remove their seeds. Cut them into thin slices.
Cut the chicken breasts in half horizontally, place them between plastic sheets, one at a time, and pound them until they are about a ¼ inch thick. Season them with salt and pepper.
Prepare a dredging station. In the first bowl place the flour, salt, and pepper. In the second bowl place the eggs. In the third bowl, place the breadcrumbs, cheese, and spices.
Fill a cast iron skillet with a ¼ inch of vegetable oil, heated on high heat. Dredge each piece of chicken in the flour, eggs, and breadcrumbs. The oil is hot when a small piece of chicken sizzles immediately when placed in the oil. Fry the chicken until it is golden, on each side, and cooked through.
Drain the cooked chicken on a wire rack.
In a food processor, mix the vinaigrette ingredients.
To serve the chicken, top it with tomato slices, mozzarella, roasted peppers, and olives. Then, drizzle some vinaigrette on top. Serve the chicken on top of spaghetti tossed with pomodoro sauce.