In a 4-quart saucepan over medium heat add the butter, onion and garlic.
Cook until softened, approximately 10 minutes.
Add green chickpeas and 4 cups of stock and simmer uncovered until the beans are tender, 8-10 minutes.
Stir in basil, heavy cream, and remaining cup of stock. Remove from heat.
In a blender, purée soup in batches until smooth. Add salt to taste. You can freeze batches to either microwave or warm up later.