Melt butter in a large pot over medium heat. Add leek and cook until soft, about 5 minutes. Add garlic and cook a minute more. Stir in broth.
Add potato, cover, and cook until very tender, about 12 minutes. Add zucchini, cream, salt and pepper. Cover and continue cooking until zucchini is just tender, 5 minutes more.
Blend with an immersion blender or carefully transfer to standing blender (work in a few batches unless you have a Vitamix or something similar with steam vents). Blend on high speed until smooth.
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Notes
Ensure your potatoes cook well and are completely soft before blending. This will help ensure you get a silky and creamy texture to your soup.Cook the garlic gently and only for a minute or so. You don't want it to burn, or it will turn the soup a little bitter.Blend the soup in batches unless you have a pro machine with vents.Recommended toppings/pairings: grated fresh parmesan cheese, black pepper, croutons, or a melty grilled cheese sandwich.