Cut the broccoli into small pieces. Add to a medium saucepan with 1 1/2 cups of water. Cook until tender about 8 to 10 minutes.
While the broccoli is cooking start the soup base. Add the butter and onion to a large skillet.
Cook the onion over medium heat for 3 to 5 minutes until it is tender.
Add the flour and pepper to the skillet and stir until well combined. Cook for about 1 minute.
Slowly add the milk stirring constantly. Cook until the soup base begins to thicken slightly.
Turn the heat back to medium and add the cheese and bouillon cubes and stir until the cheese is melted.
Once the broccoli is tender remove from the heat do not remove the water. With an immersible blender chop the broccoli leaving a few larger pieces.
Add the broccoli and the water to the soup and blend in. Continue to cook for about 10 minutes. Serve.