Melt butter in a medium-sized stock pot over medium heat. Add onion and saute for about 5 minutes or until translucent.
Add garlic and saute for another minute or two, stirring frequently.
Add zucchini and saute for 4-5 minutes, stirring frequently.
Add chicken broth and lemon zest, bring to a boil and quickly reduce heat to a gentle simmer. Simmer until zucchini are tender and cooked through, about 10 minutes.
Add basil and stir in.
Puree well with an immersion blender. Alternatively, transfer small batches to a blender, blend well and return to stock pot.
Add salt and pepper, to taste.
Serve hot or chilled in individual bowls and add any additional seasonings, to taste.