Peel and wash the potatoes and cut them roughly into pieces. Cover and cook in little boiling salted water for about 20 minutes. Wash tarragon, shake dry. Pluck the leaves from the stems and chop them, except for a little bit for garnishing.
Warm up the milk. Drain the potatoes and press them through a potato ricer. Add crème fraîche, 2 1/2 tablespoons mustard, tarragon and milk and stir in. Season to taste with salt. Serve and garnish with tarragon and remaining mustard.