Season the chicken. Pat the chicken dry. Toss with 1/2 teaspoon salt, pepper, and Italian seasoning. This simple step adds flavor and helps the chicken brown.
Sear for flavor. Heat the olive oil or butter in a large, wide pot or deep skillet over medium-high heat.
Add the chicken in a single layer and cook for 3–4 minutes, stirring once or twice, until lightly browned. It doesn’t need to be cooked through yet. Transfer to a plate.
Sauté the garlic. Lower the heat to medium.
If the pot looks dry, add a splash more oil. Add the garlic and cook for 30–45 seconds until fragrant. Don’t let it burn.
Add broth and pasta. Pour in the chicken broth and scrape up any browned bits.
Stir in the dry pasta and the browned chicken (and any juices). Bring to a strong simmer.
Simmer and stir. Reduce heat to medium-low. Cover partially, and cook for 10–12 minutes, stirring every 2–3 minutes to prevent sticking.
Cook until the pasta is just shy of al dente. If the pot looks dry before the pasta is tender, add 1/4 cup hot water at a time.
Make it creamy. Stir in the heavy cream and simmer uncovered for 2–3 minutes to thicken slightly. The sauce will continue to thicken as it cools.
Add the cheese. Remove the pot from heat.
Gradually stir in the Parmesan until melted and smooth. Add lemon juice and red pepper flakes if using. Taste and adjust with salt and pepper.
Finish and serve. Let the pasta rest for 2–3 minutes to set up.
Sprinkle with parsley and extra Parmesan. Serve hot.