Step 1: Heat olive oil in a large skillet over medium-high heat. Add the chicken and cook the brown on both sides. Add the garlic, stir and cook for one additional minute. Season with salt and pepper.
Step 2: Add the chicken broth and half and half. Bring the dish to a simmer then add the pasta. Stir occasionally, for 6 to 7 minutes until the pasta starts to soften.
Step 3: Add the broccoli, cover and cook until the pasta is al dente (about an additional 7 minutes.) Be sure to keep the pan covered to ensure that the pasta cooks evenly.
Step 4: Add the cheese and stir until everything is melted. Serve immediately or let it sit a little while longer to thicken the sauce.