Total Time: 33 mins
1. Heat oil in a large saucepan over medium-high heat. Add garlic and onion; cook, stirring occasionally, until tender, 1 to 4 minutes. Add lemon juice and cook for 1 minute.
2. Add 3 3/4 cups cucumber slices, broth, salt, pepper and cayenne; bring to a simmer. Reduce heat and cook at a gentle simmer until the cucumbers are soft, 6 to 8 minutes.
3. Transfer the soup to a blender. Add avocado and parsley; blend on low speed until smooth. (Use caution when pureeing hot liquids.)
4. Pour into a serving bowl and stir in yogurt. Chop the remaining 1/4 cup cucumber slices.
5. Serve the soup warm or refrigerate and serve it chilled. Just before serving, garnish with the chopped cucumber and more chopped parsley, if desired.
There's no reason to only use cucumbers raw—they are wonderful sautéed then pureed with avocado for a silken-textured soup that's good warm or cold.