Chop all vegetables: potatoes, carrots and celery (about 2 cups each), broccoli (or a combination of broccoli and cauliflower), and onion.
Place chopped vegetables and chicken broth into crockpot and cook on low for 4-6 hours or until vegetables are soft.
About 30 minutes before serving, prepare sauce: Melt butter in a saucepan. Add flour, mustard, salt, and pepper; stir until combined. Slowly stir in milk and cook on medium heat until thickened.
Add sauce to crock pot along with cheese. Stir until cheese is melted and fully combined.