Cook the penne pasta according to package instructions until al dente. Drain and set aside, reserving 1/2 cup of pasta water.
In a large skillet, heat the olive oil over medium heat. Add the chicken pieces, season with salt and pepper, and cook until browned and cooked through, about 5-7 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add the minced garlic and red pepper flakes (if using). Sauté for about 1 minute until fragrant, being careful not to burn the garlic.
Pour in the heavy cream and bring to a simmer. Stir in the grated Parmesan cheese until melted and smooth. If the sauce is too thick, add some reserved pasta water to reach desired consistency.
Return the cooked chicken to the skillet and add the drained pasta. Toss everything together until well coated in the sauce. Adjust seasoning with salt and pepper as needed.
Serve immediately, garnished with chopped parsley.