Bring water to a boil in a large stockpot. Add pasta; cook 5 minutes. Add broccoli; cook an additional 5 minutes or until pasta is done; drain.
While pasta cooks, lightly spoon flour into a dry measuring cup; level with a knife. Place flour in a medium saucepan; gradually add milk, stirring with a whisk until blended. Cook over medium heat 8 minutes or until mixture is thick, stirring frequently.
Remove from heat; stir in cheese and next 4 ingredients (cheese through pepper). Combine pasta mixture, cheese sauce, and ham.