Process first 4 ingredients in a food processor or blender until smooth, stopping to scrape down sides as needed.
Stir together shrimp, celery, green onions, and mayonnaise mixture. Cover and chill until ready to serve. Garnish, if desired.
Marian's tip: Prepare extra basil mayonnaise (the first four ingredients in Basil Shrimp Salad), and use it as a spread for the ultimate bacon, lettuce, and tomato sandwich.