Bring a large pot of water to a rolling boil over high heat (this takes about 10 minutes). Add 1 tablespoon of salt, then add pasta and cook according to package directions until al dente, typically 8 to 10 minutes. Reserve 1 cup of pasta water before draining. Drain pasta and set aside.

While pasta cooks, heat a 12-inch skillet over medium heat and melt 2 tablespoons butter. Add chicken pieces in a single layer, season with salt and pepper, and cook for 6 to 8 minutes, stirring every 2 minutes, until golden brown with internal temperature of 165°F and no pink remains. Remove chicken to a plate and set aside.

In the same skillet, add remaining 2 tablespoons butter. Once melted, add minced garlic and diced onion, stirring frequently for 3 to 4 minutes until onion is translucent and garlic is fragrant but not browned.

Pour in heavy cream and chicken broth, stirring to combine and scrape up any browned bits. Add Italian seasoning and red pepper flakes. Let sauce simmer gently for about 5 minutes until it reduces by about one-third and coats the back of a spoon. If sauce becomes too thick, add reserved pasta water to adjust consistency.

Return cooked chicken and drained pasta to the skillet with the sauce. Toss everything together gently but thoroughly using tongs, ensuring pasta and chicken are well coated. Cook for another 2 minutes to meld flavors. Taste and adjust seasoning with salt and pepper if needed.

Remove from heat and sprinkle grated Parmesan cheese over the top, gently tossing to help it melt into the hot pasta. Let dish rest for 2 to 3 minutes before serving. Garnish with fresh chopped parsley if desired. Serve immediately while hot and creamy.