In a large skillet, heat oil over medium heat. Add garlic and cook, stirring often, until it begins to soften (about 3 minutes). Add chicken, basil, salt, and crushed red pepper. Cook, stirring often, until chicken is cooked (10 to 15 minutes).
Cook pasta according to directions.
While pasta is cooking, mince the tomatoes. Add tomatoes, broth, and wine to chicken. Reduce heat to medium-low and simmer gently until mixture begins to thicken (about 5 minutes). Stir in whipping cream and cheese and simmer for 2 minutes more.
Place drained pasta in pan with chicken. Mix gently and transfer to a serving platter. Serve with additional Parmesan cheese at the table.