Bring a large pot of salted water to a boil. Cook the penne or rigatoni until al dente according to the package directions. Reserve 1/2 cup pasta water, then drain.

While the pasta cooks, season the chicken pieces evenly with Italian seasoning, paprika, salt, and black pepper.

Heat the olive oil in a large skillet over medium-high heat. Add the chicken in a single layer and cook until browned and fully cooked, turning as needed. The thickest pieces should reach 165°F. Transfer to a plate.

Reduce the heat to medium-low. Melt the butter in the same skillet, add the garlic, and cook for about 30 seconds until fragrant. Pour in the chicken broth, scrape up the browned bits, then add the heavy cream and bring to a gentle simmer.

Reduce the heat to low. Gradually stir in the freshly grated Parmesan until melted and smooth. If needed, add reserved pasta water a little at a time to adjust the consistency. Do not boil the sauce after adding the cheese.

Return the chicken to the skillet and add the drained pasta. Toss until evenly coated in the garlic Parmesan sauce. Finish with chopped parsley, black pepper, and additional Parmesan if desired. Serve immediately.