Set aside 2 to 3 tarragon sprigs for garnish. Pluck the remaining leaves from the branches.
Remove the skin from the shallot and chop finely. In a medium frying pan, sauté in the hot olive oil until light yellow. Extinguish with the Noilly Prat and turn down for 2 to 3 minutes. Pour in the soup, add the tarragon leaves and let the whole thing bubble up once, then cool to hand heat.
In the meantime, rinse the cucumber and cut it about 8 cm small for the garnish. Cut this piece, unpeeled, into paper-thin slices and set aside. Peel the remaining cucumber, cut in half lengthwise, scrape out the seeds and cut the cucumber flesh into chunks.
Blend the cooled soup, peeled cucumber pieces, tarragon mustard and crème fraîche in a hand blender or possibly with a hand blender. Season the soup with salt and pepper and chill for at least 2 hours.
Serve the soup in plates or cups. Garnish with cucumber slices and tarragon leaves.
The soup can be garnished with sliced salmon ham or cooked shrimps. Important to know: Depending on the season, the flavor intensity of tarragon varies greatly: If you need a whole bunch in early summer, half of it can be more than enough in midsummer or fall.
Tip: It is best to use your favorite ham – then your dish tastes twice as good!