Bring a large pan of water to the boil and cook the pasta following pack instructions, adding the broccoli florets to the pan for the final 4 mins. Drain and set aside.
Meanwhile, make the sauce. Heat the oil in a large pan and cook the onion for 5 mins to soften, then stir in the garlic and cook for 1 min more. Stir in the ham, cream and mustard, then bring to the boil. Add the pasta and broccoli, then stir in the cheese, coating everything in the sauce.