Heat butter in medium stockpot. Add onions; cook over medium heat until softened. Add broccoli and chicken stock or water.
Increase heat to high; cook until mixture comes to a boil. Reduce heat to medium-low and simmer until broccoli is tender.
Using an immersion blender, purée until mixture reaches desired consistency.
Stir in Cream Sauce Base, salt, pepper and cheese. Continue heating at medium-low heat until soup reaches 165°F.