Roughly chop the cucumbers, bell peppers, tomatoes and red onions.
Blend each ingredient individually in a food processor until puréed, transferring the puréed ingredients into a large bowl. (Be careful not to over-process the ingredients or the gazpacho will be too thin.)
Add the tomato juice, garlic, vinegar, olive oil, salt and pepper to the bowl with the puréed veggies, stirring until well combined. Cover the gazpacho and refrigerate it until chilled.
Once the gazpacho is chilled, serve it topped with chopped hard-boiled eggs (optional).
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