To the basin of a 6-8 quart slow cooker, add the chopped onion, broccoli, carrots, celery, salt, pepper, and chicken stock.
Cover and cook on LOW for 5 hours or HIGH for 3 hours.
After the set cook time, to a small microwave safe bowl, melt the butter and then whisk in the flour.
Pour the butter mixture into the slow cooker.
Stir in the milk and shredded cheese.
Replace cover and cook another hour or until the cheese is melted.
Stir until smooth and then serve.
