Bring a large pot of well-salted water to a boil. Cook the penne according to package directions until just al dente, pulling it about 1 minute early. Drain and set aside.

Pat chicken breasts dry and season both sides with salt and pepper. Heat 1 tablespoon olive oil in a large skillet over medium-high heat. Cook chicken 5 to 6 minutes per side until golden and cooked through. Transfer to a cutting board, rest 5 minutes, then slice into thin strips.

In the same skillet, heat the remaining tablespoon of olive oil over medium heat. Add minced garlic and cook for 1 minute until fragrant. Add red pepper flakes and cook 30 more seconds.

Pour in diced tomatoes, heavy cream, and chicken broth. Stir to combine and bring to a gentle simmer. Cook uncovered for 5 to 7 minutes, stirring occasionally, until the sauce thickens slightly.

Add the drained pasta and sliced chicken to the skillet. Toss well to coat everything in the sauce.

Remove from heat. Stir in shredded mozzarella and Parmesan until melted and creamy. Fold in fresh basil, garnish with parsley if desired, and serve immediately.