01 - Bring a large pot of salted water to a boil. Cook the pasta according to package instructions until al dente. Drain, reserving ½ cup pasta water.
02 - While the pasta cooks, pat chicken breasts dry, season both sides with salt and pepper.
03 - Heat olive oil in a large skillet over medium heat. Add chicken breasts and cook 5-7 minutes per side, until golden and cooked through (internal temperature 165°F). Remove from the pan, 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. Gradually whisk in milk and heavy cream. Bring to a simmer and cook, stirring, until slightly thickened, about 3-4 minutes.
06 - Add Parmesan cheese and red pepper flakes (if using). Stir until cheese melts and sauce is smooth. If needed, add reserved pasta water a little at a time to reach desired consistency.
07 - Add cooked pasta and sliced chicken to the sauce. Toss to coat evenly. Sprinkle with fresh parsley and serve immediately.