Carefully chop the tomatoes, bell peppers, cucumbers, and onions into small, even-sized cubes. Dice up some basil as well. Reserve some for garnish.
In a blender or food processor, combine the tomatoes, red and green bell peppers, cucumber, basil, onion, and garlic. Blend until completely smooth.
With the blender still running, drizzle in the olive oil and sherry vinegar. Add the salt and a few grinds of black pepper. (Note: This photo was taken without the top on and blender was set on pause).
Taste the gazpacho and adjust the seasoning with additional salt, pepper, or vinegar as needed.
If you prefer a smoother gazpacho, pour the mixture through a fine-mesh sieve to remove any remaining bits of skin or seeds. (optional)
Transfer the gazpacho to a large bowl or pitcher, cover, and refrigerate for at least 2 hours, or until well chilled.
Ladle the gazpacho into bowls and top with your desired garnishes. Garnish with fresh tomatoes, cucumbers, green peppers, and basil. (optional)