Process lemon juice, chopped shallot, chopped fresh tarragon, red wine vinegar, sugar, Dijon mustard, salt, and pepper in a blender until smooth. With blender running, add olive oil in a slow, steady stream, processing until smooth. Turn off blender; add pistachios, and pulse until pistachios are finely chopped.
Drizzle 1 lb. grilled asparagus with 3 to 4 Tbsp. vinaigrette, or try it over grilled salmon or other meat. Store any remaining vinaigrette in an airtight container in refrigerator 3 to 5 days.