Cover each chicken breast with plastic wrap and pound each piece to an even thickness, about an inch or so, to help the chicken cook more evenly. Remove the plastic (you do not want to cook that!) and sprinkle each side of the chicken breast with salt and pepper.
Prepare the shallots, garlic, tomatoes and basil and set aside. Meanwhile bring a large pot of water to a boil over high heat and cook your favorite pasta according to package instructions.
In a large skillet or Dutch oven, heat the olive oil over medium high heat. When hot, add the chicken and pan-fry each side for several minutes until chicken is just cooked and the chicken is nice and brown on the outside. When chicken is done, remove from skillet and set aside.
Turn heat to medium and add butter to the skillet. Stir in the shallots and garlic and cook for approximately 3-4 minutes. Add the roasted red peppers, chopped tomatoes with juice, cherry tomatoes, and salt and pepper. Stir well. Mix in the fresh basil, crushed red pepper, dry basil, dry parsley and lemon, and stir. Simmer to cook the roasted peppers and tomatoes down to a chunky sauce-like mixture, stirring occasionally.
Finally, return the chicken breasts to the skillet and allow it to cook with the sauce for a few minutes before serving.
Garnish with fresh parsley and freshly grated Parmesan cheese.