Set a large pot of salted water to boil. Add pasta and cook according to package directions. Add broccoli to boiling water with pasta during last 3-4 minutes. Drain and set aside in a colander.

In the same large pot set over medium heat, melt butter. Stir in flour. Cook mixture, stirring constantly, for 1 minute. Whisk in milk, then season with onion powder, garlic powder, salt and pepper. Increase heat to medium-high and cook mixture, stirring constantly until it boils and thickens. Remove from heat and stir in cheese until melted. Add pasta, broccoli and ham, tossing to evenly coat.

Enjoy!