Bring a large pot of salted water to a boil. Add the pasta and cook according to package directions until al dente. Drain well and set aside.

While the pasta cooks, season the chicken pieces with 1/2 teaspoon salt and 1/4 teaspoon black pepper.

Heat olive oil in a large skillet or Dutch oven over medium-high heat. Add the chicken and cook until golden brown and cooked through, about 5-7 minutes. Remove chicken from the skillet and set aside.

Reduce heat to medium. Add butter to the same skillet. Once melted, add the minced garlic and cook for about 1 minute until fragrant, being careful not to burn it.

Sprinkle the flour over the garlic and butter, stirring constantly for 1 minute to create a roux.

Gradually whisk in the chicken broth, scraping up any browned bits from the bottom of the pan. Bring to a simmer, then slowly whisk in the heavy cream. Continue to simmer for 3-5 minutes, or until the sauce slightly thickens.

Stir in the 1 cup of grated Parmesan cheese, remaining 1/2 teaspoon salt, and 1/4 teaspoon black pepper until the cheese is melted and the sauce is smooth.

Add the cooked chicken and drained pasta to the skillet with the sauce. Toss gently to coat everything evenly.

Serve immediately, garnished with fresh chopped parsley and extra Parmesan cheese, if desired.