In 2 to 3-quart saucepan over medium heat, melt butter. Add onion; saute 5 minutes. Add potatoes, water and bouillon cubes. Bring to boil, reduce heat, cover and cook until potatoes are just tender, about 15 minutes.
Remove 1 cup of potato cubes with slotted spoon; set aside.
Pour contents of saucepan into container of electric blender. Holding lid down tightly, blend until smooth; return to saucepan.
Mix in reserved potatoes and the broccoli. Over medium-low heat gradually add cheese, stirring until heated through and cheese is completely melted. Season with salt and pepper.
Notes
If requiring a gluten-free recipe, check the label of the indicated (*) recipe ingredients to ensure they are gluten-free.