Drain pickled vegetables, reserving 1/4 cup liquid.
Pulse pickled vegetables, onion, if desired, and next 10 ingredients in a food processor until coarsely chopped. Stir in reserved vegetable liquid and, if desired, roasted red peppers; cover and chill 8 hours. Chill leftover mixture up to 2 weeks.
Note: We used mixed pickled vegetables that contained cauliflower, onion, carrot, pepper, and celery.