Bring a large pot of salted water to a rolling boil. Cook the pasta until al dente, about 8 to 10 minutes. Before draining, scoop out and save 1 cup of the starchy pasta water. Drain and set the pasta aside.

Heat a large skillet over medium heat and melt 2 tablespoons of butter. Add the diced chicken in a single layer. Season the chicken with salt and pepper. Let it sear without moving for 2 minutes, then stir and cook until golden and cooked through, about 4 to 6 more minutes. Transfer the chicken to a plate.

In the same skillet, add the remaining 2 tablespoons of butter. Add the minced garlic and diced onion. Sauté until the onion is translucent and fragrant, about 3 to 4 minutes.

Pour in the heavy cream and chicken broth. Stir in the Italian seasoning and red pepper flakes. Bring the sauce to a gentle simmer and let it reduce and thicken for 4 to 5 minutes.

Return the cooked chicken and drained pasta to the skillet. Toss everything to combine and let it warm together for 1 to 2 minutes so flavors meld. Taste and adjust salt and pepper.

Remove the pan from the heat and sprinkle the grated Parmesan over the pasta. Toss gently so the cheese melts into the sauce and creates a glossy coating. Garnish with chopped fresh parsley and serve immediately.