Add onions and cook until softened about 3-5 minutes.
Stir in broccoli, and pour chicken broth over broccoli.
Simmer until broccoli is tender, about 10 minutes.
Reduce heat, and stir in processed cheese cubes, and continue to stir until melted.
Turn heat to low, and stir in milk or half and half, garlic powder, and dry mustard.
Taste and adjust with seasonings to taste preference.
Thicken soup by combining water and corn starch in a small bowl, and stirring until cornstarch is dissolved. Slowly, stir mixture into soup; cook, stirring over low heat until thick.
Notes
To make with real cheddar cheese see instructions in post copy.