Pulse first 4 ingredients in a food processor until finely chopped. Add vinegar and next 5 ingredients, and process until well blended and smooth, stopping to scrape down sides. With processor running, pour oil in a slow, steady stream, processing until blended. Stir in paprika, if desired.
Cover and chill 6 to 8 hours.
Stir chilled sauce; pour over shrimp, gently tossing to coat. Serve on lettuce leaves.