Heat olive oil in a large pan over medium-high heat and add garlic.
Saute until fragrant, about 30 seconds.
Sprinkle chicken with salt and pepper then add to the pan.
Saute until golden brown, about 5 minutes.
Add white wine to deglaze using a wooden spoon to scrape up any browned bits from the bottom of the pan.
Reduce heat to low and simmer until liquid reduces by half.
Stir in chicken stock and continue simmering for 5 minutes.
Check the sauce for seasoning and add salt and pepper to taste.
Bring a large pot of salted water to a boil and add pasta.
Cook according to package instructions, adding the broccoli florets to the pot two minutes before the end of the cooking time.
Drain the broccoli and pasta but do not rinse off the cooking liquid.
Add cooked broccoli and pasta to the pan with chicken in white wine sauce.
Add shredded mozzarella and toss until it begins to melt.
Place in a large shallow bowl and garnish with Parmesan cheese to serve.