In a large deep skillet, heat the oil and butter together over medium high heat.
In a medium bowl, mix together the flour, salt and pepper.
Lightly dredge the chicken cubes in the flour mixture and place into the hot pan.
Brown on all sides, cooking for a total of 4-5 minutes or until cooked through and no longer pink in the center.
Transfer chicken to a plate and add in minced garlic. Cook for 30 seconds.
Slowly pour in chicken broth and scrape up any browned bits from the bottom of the pan.
Bring it to a boil and add in the pasta.
Cover the pan with a lid and cook for 10 minutes.
Add in the broccoli florets and cover. There should be about 1 cup of liquid in the pan. Add a little water if needed to make up the difference.
Cook for 4-5 minutes or until broccoli is tender.
Reduce heat to medium low and pour in half and half.
Sprinkle in cheese and stir until completely melted.
Season with more salt and pepper if needed.
Let it simmer for 5 minutes to allow the sauce to thicken.
Add in chicken and stir to coat.
Serve with more grated parmesan cheese.