1. Rinse mushrooms and pat dry with paper towels. Trim and discard any discolored areas and tough stem ends (whole stems for shiitakes). Working in batches, pulse mushrooms in a food processor until finely chopped (or chop with a sharp knife).
2. In a 10- to 12-inch nonstick frying pan over medium heat, melt butter. Add onion and stir often until limp, about 5 minutes. Add chopped mushrooms and sprinkle evenly with salt. Stir often until juices have evaporated and mushrooms are beginning to brown, about 10 minutes; remove from heat. Grind in pepper to taste.
3. In a glass measure, stir together sour cream, vinegar, and tarragon. Pour into mushroom mixture and stir to mix. Serve warm or at room temperature.