Cook the fettuccine or spaghetti 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-high heat. Season the chicken pieces with salt and pepper, then add them to the skillet. Cook for about 5-7 minutes, or until the chicken is golden brown and cooked through. 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 chicken broth and bring to a simmer, scraping up any browned bits from the bottom of the skillet. Let it cook for about 2-3 minutes.
Reduce the heat to low and add the butter, stirring until melted and combined. Return the cooked chicken to the skillet and mix well.
Add the cooked pasta to the skillet, tossing to coat in the garlic butter sauce. If the pasta seems dry, add a little reserved pasta water until you reach your desired consistency.
Stir in the grated Parmesan cheese and mix until well combined. Adjust seasoning with salt and pepper if needed.
Serve immediately, garnished with fresh parsley.