Place the peppers in the bowl of a food processor and pulse a few seconds, until finely chopped, but not pureed. It is nice if some pieces are larger than others. Transfer to a large soup pot or bowl. Repeat process with onion and cilantro, celery and green onion, cucumber and garlic, and tomatoes.

Mix the chopped vegetables well and transfer about 2/3 of the mixture in two batches back to the food processor. Add to one of the batches in the work bowl the V8 juice, olive oil, vinegars, salt, pepper, paprika and Cholula hot sauce. Puree the mixture until mostly smooth and olive oil is worked through emulsified. Add it back to the soup pot. Mix with the finely chopped vegetables and chill at least 3 hours, but preferably overnight. Taste and adjust hot sauce, salt, cilantro and juice to thin before serving. Garnish with lemon wedges. Soup will keep in the refrigerator for several days.