Prepare pasta and broccoli according to package directions.
Meanwhile, melt butter in a large saucepan over medium heat. Gradually whisk in flour until smooth; cook, whisking constantly, 1 minute. Gradually whisk in milk and next 3 ingredients; cook, whisking constantly, 8 to 10 minutes or until thickened.
Remove from heat.
Gradually stir in Cheddar cheese, stirring until cheese is melted and sauce is smooth. Stir in ham, hot cooked pasta, and broccoli.