Chop broccoli into small pieces and microwave on high in a small amount of water for about two minutes. Dice potatoes and boil until cooked through, about 10 minutes. Drain. Grate cheese and set aside. Combine chicken broth and milk. Microwave for about three minutes or until liquid boils. Saute onion in butter until tender. Stir in flour, salt, and pepper. Cook stirring constantly until smooth and bubbly. Add liquid all at once. Stir to blend. Add broccoli and potatoes. Simmer stirring constantly until thoroughly heated. Remove from heat, add cheese and stir until melted.
