Place the avocado, lemon juice, cilantro, garlic, yogurt, salt, pepper, cumin, cayenne, and water in your food processor. Process until very smooth, about 1 minute, stopping once to scrape the sides of the bowl with a spatula.
Check the consistency and, if desired, add up to ¼ cup more water and process to combine.
Cover and refrigerate the soup for 30 minutes. Mix it again, divide it among 4 individual bowls, garnish with cilantro leaves, and serve.
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Notes
I recommend using Haas avocado. It's creamy, flavorful, and not as watery as other avocado varieties.
It's OK to use regular (non-Greek) yogurt, but then you will need to add less or even no water.
While you could serve the soup immediately, keeping it in the fridge for 30 minutes before serving allows the flavors to meld and dramatically improves its texture and flavor. It tastes better when it's cold. So, I highly recommend you don't skip this step.
You can keep the leftovers in an airtight container in the fridge for 1-2 days. Remix them before serving. If the soup has thickened too much while being stored, add 1-2 tablespoons of water.