Bring a large pot of salted water to a boil. Add the penne pasta and cook according to package instructions until al dente, about 10-12 minutes. Drain and set aside.
While the pasta cooks, heat olive oil in a large skillet over medium-high heat.
Season the chicken pieces with salt and black pepper.
Add the chicken to the skillet and cook for 6-8 minutes, stirring occasionally, until the chicken is cooked through and lightly browned. Remove the chicken from the skillet and set aside.
Reduce heat to medium and add the minced garlic and red pepper flakes to the same skillet. Cook for 1 minute until fragrant, stirring constantly to avoid burning.
Pour in the crushed tomatoes and stir to combine. Let the sauce simmer for 5 minutes.
Stir in the heavy cream and grated Parmesan cheese. Cook for another 3 minutes until the sauce is creamy and heated through.
Return the cooked chicken to the skillet and stir to coat with the sauce.
Add the cooked pasta to the skillet and toss everything together until well combined.
Remove from heat and stir in the chopped fresh basil and parsley.
Allow the dish to cool completely before transferring to airtight containers for storage.
Refrigerate for up to 3 days or freeze for up to 1 month. Reheat thoroughly before serving.