Roughly chop all vegetables into 1-inch cubes.
Put each vegetable separately into a food processor fitted with a steel blade and pulse just until coarsely chopped. Do not over-process!
After each vegetable is processed, combine them in a large bowl and add the garlic, tomato juice, vinegar, olive oil, salt, and pepper.
Mix well and chill before serving. The longer gazpacho sits, the more the flavors develop.
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