Bring a large pot of salted water to a boil. Cook pasta according to package instructions until al dente. Drain, reserving 1 cup of pasta water.

In a large skillet over medium-high heat, melt 2 tablespoons of butter. Add chicken pieces, season with salt and pepper, and cook until golden brown and cooked through, about 5-7 minutes. Remove chicken from skillet and set aside.

In the same skillet, melt remaining 2 tablespoons of butter. Add minced garlic and sauté for about 30 seconds until fragrant. Whisk in flour and cook for 1 minute to form a roux.

Gradually whisk in chicken broth, bringing the mixture to a simmer. Cook until slightly thickened, about 2-3 minutes.

Stir in heavy cream and grated Parmesan cheese, cooking until the cheese is melted and the sauce is smooth. Season with salt and pepper to taste.

Return cooked chicken to the skillet, followed by the drained pasta. Toss to combine, ensuring the pasta is evenly coated with the sauce. If needed, add reserved pasta water to achieve desired consistency.

Garnish with chopped fresh parsley before serving.