Prepare the pasta according to the package directions, the broccoli will cook the last few minutes in the same pot, when the pasta is almost done cooking.
(Cook broccoli in the pasta water for the last 1-2 minutes for small pieces and larger florets 3-4 minutes) cook to desired tenderness)
Drain the pasta with broccoli in a colander when finished cooking to the desired doneness.
In the pot, place 2 tablespoons butter with ham along with onion, garlic, and paprika, and cook for 1 minute while stirring. (brown the ham longer for more flavor)
add in the chicken bouillon and flour and whisk in the milk slowly developing a creamy sauce.
Add in cheese and stir until smooth.
Add in the past and broccoli, and turn off the burner.
Stir to coat the pasta and broccoli in the cheese sauce.
Add salt and black pepper to taste.