Cook the whole wheat 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, season with salt and pepper, and cook until browned and cooked through, about 5-7 minutes.
Add the minced garlic and red pepper flakes to the skillet, cooking for an additional 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 cooked pasta, spinach, and Parmesan cheese. If the mixture is too dry, add some reserved pasta water until desired consistency is reached.
Toss everything together until well combined and the spinach is wilted. Adjust seasoning with salt and pepper if needed.
Serve hot, garnished with fresh parsley and additional Parmesan if desired.