Cook pasta in salted boiling water until al dente. Reserve 1 cup pasta water. Drain and set aside.
Season chicken with salt, pepper, and red pepper flakes. Sear in olive oil over medium-high heat, 5–6 min per side. Rest, then slice.
In the same pan over medium heat, sauté garlic for 60 seconds. Add broth and cream. Simmer 2–3 minutes.
Add Boursin cheese and stir until fully melted and smooth.
Add cherry tomatoes and spinach. Stir until spinach wilts.
Toss in cooked pasta and chicken. Add pasta water as needed for creaminess.
Serve with Parmesan, fresh herbs, and cracked black pepper.