In a blender, combine the avocados, vegetable broth, Greek yogurt, lemon juice, fresh basil, minced garlic, salt, black pepper, and cayenne pepper (if using). Blend until smooth and creamy.

Taste and adjust seasoning if necessary, adding more salt or lemon juice to your preference.

Transfer the soup to a bowl and cover it with plastic wrap. Chill in the refrigerator for at least 1 hour to allow the flavors to meld.

Once chilled, stir the soup gently and serve in bowls. Drizzle with olive oil and garnish with fresh basil leaves and lemon slices.