Prepare the Cucumbers:
Peel, seed, and chop the cucumbers. Set aside a small amount for garnish if desired.
Blend the Soup:
In a blender or food processor, combine the chopped cucumbers, Greek yogurt, cold water, minced garlic, chopped shallot or red onion, fresh dill, lemon juice, and olive oil. Blend until smooth.
If using, add the avocado for extra creaminess and blend again until smooth.
Season the Soup:
Taste and season with salt and freshly ground black pepper. Blend again to combine.
Chill the Soup:
Transfer the soup to a bowl and cover. Refrigerate for at least 1 hour to allow the flavors to meld and the soup to chill thoroughly.
Serve:
Before serving, stir the soup and adjust the seasoning if necessary.
Ladle the chilled soup into serving bowls.
Garnish with the reserved cucumber, a sprinkle of fresh dill, and a drizzle of olive oil if desired.