Cut cucumber, onion, bell peppers, and tomatoes into medium-sized chunks. For a chunky soup, place veggies directly in a bowl.
But, for a smoother soup, place the first 7 ingredients in a large food processor fitted with a steel blade. Pulse processor six or seven times for a slightly chunky gazpacho.
Puree for a minute or two for a smoother soup. Add avocado and pulse until smooth.
Transfer to a large bowl and add the remaining ingredients.
Stir well. Chill for several hours or overnight. When ready to serve, ladle into soup bowls or mugs and garnish with a dollop of plain Greek yogurt, cilantro leaves, and chopped cherry tomatoes.