Bring large pot of salted water to boil and cook penne 10 to 12 minutes until done.
Add broccoli florets to boiling pasta water during the last 3 minutes of cooking the pasta.
Drain pasta and broccoli together in colander and save 1 cup of the starchy pasta water.
Season chicken breasts with salt and pepper then cook in olive oil 6 to 7 minutes per side.
Remove chicken from skillet and let rest 5 minutes then slice into thin strips or bite-sized pieces.
Melt butter in same skillet then add minced garlic and cook 1 minute until it smells amazing.
Pour heavy cream into skillet and simmer 3 to 4 minutes until sauce begins to thicken slightly.
Reduce heat to low and gradually add Parmesan cheese stirring constantly until melted and sauce is smooth.
Add drained pasta and broccoli to sauce and toss with tongs until everything is coated really well.
Add sliced chicken to pasta and toss again and adjust consistency with reserved pasta water if needed.
Serve immediately and garnish with extra Parmesan cheese and freshly cracked black pepper on top.