01 - Bring a large pot of salted water to a boil. Cook pasta according to package directions until al dente. Drain, reserving ½ cup pasta water.
02 - While pasta cooks, pat chicken breasts dry and season both sides with salt and pepper.
03 - Heat olive oil in a large skillet over medium heat. Add chicken and cook 5–7 minutes per side until golden and cooked through (internal temperature 165°F). Remove, let rest 5 minutes, then slice thinly.
04 - In the same skillet, melt butter over medium heat. Add garlic and sauté 1–2 minutes until fragrant.
05 - Sprinkle in flour, whisking constantly, and cook for 1 minute to remove raw flour taste.
06 - Gradually whisk in milk and heavy cream. Bring to a simmer and cook, stirring constantly, until slightly thickened, about 3–4 minutes.
07 - Add Parmesan cheese and red pepper flakes. Stir until cheese melts and sauce is smooth. Add reserved pasta water as needed to reach desired consistency.
08 - Add cooked pasta and sliced chicken to the sauce. Toss to coat evenly. Sprinkle with fresh parsley and serve immediately.