Cook the pasta in salted water until al dente. Drain, reserve a splash of the starchy water, and set aside.
In a large skillet, heat olive oil over medium heat. Add garlic and sauté until fragrant, about 30 seconds.
Pour in the chicken broth and cream. Simmer gently, stirring, until it thickens a bit and looks cozy.
Stir in the parmesan until it’s melted into the sauce. If it’s too thick, loosen with a splash of the reserved pasta water.
Drop in the spinach and let it wilt, then add the cooked chicken. Heat through, about 2–3 minutes.
Toss the pasta into the skillet, coating it with the sauce. Season with salt, pepper, and red pepper flakes if you like a nudge of heat.
Serve warm and watch it disappear in record time. Optional: finish with a little extra parmesan on top.