Cover each chicken breast with plastic wrap and pound each piece to an even thickness, about a 1/2-inch, 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 the chicken is nearly cooked and the chicken is golden brown on the outside. When the chicken is done, remove it from the skillet and set it aside.
Reduce heat to medium and add the 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 fresh lemon juice. Stir well. Bring to a simmer, then reduce heat to low and continue to cook the sauce until it reaches a chunky sauce-like mixture. Stir occasionally.
Optional- For a smoother sauce, transfer half of the sauce mixture to a blender and pulse until smooth. Return to the pan and combine.
Nestle the chicken breasts in the simmering sauce and allow them to finish cooking for 3-5 minutes, or until the internal temperature registers 165°F as measured by a digital meat thermometer.
Garnish with fresh parsley and freshly grated Parmesan cheese and serve over cooked pasta.