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. Serve immediately.