Cook the whole wheat penne pasta according to package instructions until al dente. Drain and set aside, reserving 1/2 cup of the pasta water.
In a large skillet, heat the olive oil over medium heat. Add the chicken pieces and season with salt and pepper. Cook until browned and cooked through, about 5-7 minutes.
Add the minced garlic, oregano, basil, and red pepper flakes to the skillet. Sauté for 1-2 minutes until fragrant.
Pour in the chicken broth and bring to a simmer. Let it cook for about 3-4 minutes to reduce slightly.
Stir in the chopped spinach and cooked penne pasta. If the mixture seems dry, add some reserved pasta water to achieve the desired consistency.
Remove from heat and stir in the grated Parmesan cheese until melted and well combined.
Serve hot, garnished with fresh parsley.