Prep the chicken and aromatics. Cut the chicken into small, even pieces. Mince the garlic and chop the onion or shallot. Grate the Parmesan so it melts smoothly later.
Brown the chicken. Heat a large deep skillet or Dutch oven over medium-high.
Add oil or butter. Season chicken with salt and pepper, then cook 4–6 minutes until lightly golden and nearly cooked through. Remove to a plate.
Soften the aromatics. In the same pot, lower heat to medium.
Add a splash more oil if dry, then add onion and a pinch of salt. Cook 2–3 minutes until translucent. Add minced garlic and cook 30–60 seconds until fragrant—don’t let it brown.
Toast the seasonings. Stir in Italian seasoning and red pepper flakes.
Toast 20–30 seconds to wake up the herbs.
Add pasta and broth. Pour in the pasta and 3.5 cups of chicken broth. Scrape up any browned bits from the pot. Bring to a lively simmer.
Simmer until al dente. Cook uncovered, stirring every 1–2 minutes so the pasta doesn’t stick.
This takes about 9–12 minutes, depending on the shape. If the pot looks dry before the pasta is tender, add the remaining broth in splashes.
Return the chicken. Stir the chicken back into the pot during the last 3–4 minutes of pasta cooking so it finishes gently and stays juicy.
Add the cream. Reduce the heat to low. Stir in the heavy cream.
The sauce will look loose at first but will thicken within a couple of minutes.
Stir in Parmesan. Off the heat, sprinkle in the Parmesan a handful at a time, stirring until smooth. If adding spinach or peas, fold them in now. Let the residual heat wilt spinach or warm peas through.
Adjust and brighten. Taste and add more salt and pepper if needed.
A light squeeze of lemon or a bit of zest lifts the richness without overpowering the garlic flavor.
Finish and serve. Top with chopped parsley and extra Parmesan. Serve hot, with a simple green salad or roasted vegetables on the side.