Score the upper third of the melons in a zigzag shape and lift off the lid. Remove the core with a spoon. From the pulp, also from the lid, cut out about 40 small balls with a ball cutter and put aside. Scrape out the remaining pulp with a spoon, weigh out 300 g of it and place in a hand mixer form. Grate the lime peel, squeeze the juice from the fruit, add both to the pulp together with the powdered sugar, chili, plum wine and ice cubes.
Finely chop the tarragon leaves from three sprigs and stir into the soup with the champagne. Fill the iceberg shrimp and the melon balls into the hollowed melon, add the soup and garnish with pine nuts and tarragon sprigs.