Add zucchini, onion, garlic cloves, and chicken broth to a large pot and place a lid on it. Bring to a boil then reduce heat to medium and let it simmer for 20 minutes, stirring occasionally.
Once the zucchini is extremely softened remove the pot from the heat and use an immersion blender to blend everything into a smooth puree.
Add salt and pepper to the puree and then stir in the heavy cream.