Fill a large pot with salted water and bring it to a boil. Add the penne pasta and cook according to package instructions until al dente, usually around 10-12 minutes. Drain the pasta using a colander and set aside, reserving about 1/4 cup of the pasta water.
While the pasta cooks, dice the chicken breast into bite-sized pieces. Season with salt and black pepper to taste.
In a large skillet over medium-high heat, melt 2 tablespoons of the unsalted butter. Add the diced chicken and cook until golden brown and cooked through, about 5-7 minutes. Remove the chicken from the pan and set aside.
Reduce the heat to medium. Add the remaining 2 tablespoons of butter to the skillet. Once melted, add the minced garlic and red pepper flakes. Sauté for 1-2 minutes until fragrant and the garlic is lightly golden, being careful not to burn it.
Pour in the chicken broth to deglaze the pan, scraping up any browned bits from the bottom. Let it simmer for 2 minutes to reduce slightly. Return the cooked chicken to the skillet, stir to coat in the sauce.
Add the cooked penne pasta to the skillet. Toss everything together until well combined. If the sauce seems too thick, add a splash of the reserved pasta water to loosen it up. Stir in the grated Parmesan cheese until melted and creamy.
Sprinkle the chopped fresh parsley over the pasta for a burst of color and freshness. Serve immediately while warm with extra Parmesan on the side if desired.