Bring a large pot of salted water to a boil and cook rigatoni according to package instructions, until al dente. Reserve 1 cup of pasta water.
In a large skillet over medium-high heat, melt 2 tablespoons of butter. Add the chicken pieces and brown on all sides until cooked through, about 6-8 minutes.
Reduce heat to medium. Add the remaining 1 tablespoon of butter to the pan, then sauté the garlic for 1-2 minutes until fragrant.
Pour in the chicken broth and stir to deglaze the pan, scraping up any browned bits.
Stir in the heavy cream and bring to a gentle simmer.
Gradually stir in the grated Parmesan cheese until melted and well combined. Season with Italian seasoning, salt, and black pepper.
Add the cooked pasta to the skillet and toss to coat everything evenly in the sauce. Add a bit of reserved pasta water if the sauce is too thick.
Transfer to serving bowls and top with fresh chopped parsley.