In a large pot, heat the oil and stir in the chopped onion and minced garlic. Cook for a few minutes until the onion begins to soften.
Add diced zucchini, broth and bring to a boil.
Lower heat, cover, and simmer until tender, about 15-20 minutes.
Remove from heat and purée with an immersion blender or a normal blender. You can also use a potato masher.
Add the half & half, cream or sour cream if using.
Taste for salt and pepper and adjust to taste.