Rinse and trim ends from green onions; cut into 2-inch pieces (including tops). In a food processor or blender, purée the onions, rice vinegar, wine, mustard, oil, parsley, mint, and basil until smooth. Stir in white pepper to taste. Scrape into a small bowl; if making up to 1 day ahead, cover and chill.
Nutritional analysis per tablespoon.