Place the tomatoes, tomato paste, Italian seasoning and red pepper in a medium-sized bowl, and stir to mix well. Set aside.
Rinse the chicken with cool water and pat dry with paper towels. Place the chicken pieces on a flat surface and use a meat mallet to pound each piece to 1/4-inch thickness. Sprinkle both sides of the chicken pieces with the salt and pepper.
Coat a large nonstick skillet with olive oil cooking spray and preheat over medium-high heat. Arrange the chicken in the skillet and cook for 3 to 4 minutes on each side or until nicely browned and no longer pink inside. Transfer the chicken to a platter and cover to keep warm.
Add the wine or broth to the skillet and cook over medium-high heat for a minute or 2 or until most of the wine or broth has evaporated. Add the garlic, onions, peppers and mushrooms to the skillet and stir-fry for about 4 minutes or until the vegetables are crisp-tender. Add a little more wine or broth if the skillet becomes too dry.
Move the vegetables to one side of the skillet and return the chicken to the skillet. Arrange the vegetables over and around the chicken.
Pour the tomato mixture over the chicken and vegetables and bring to a boil over medium-high heat. Reduce the heat to low, cover and simmer for about 10 minutes, or until the flavors are well blended and the vegetables are tender. Serve hot with your choice of pasta, topping each serving with a tablespoon of Parmesan, if desired.