Place the cucumber and melon in a shaker and press with a muddler to break them up. Fill the shaker with ice and add the vermouth, shrub, syrup, lime juice, and bitters. Using some force, shake hard for 5 seconds. Using a small fine- mesh bar sieve to catch the loose ice chips, double strain into a carbonated drink maker (like the Drinkmate). Add the filtered water and follow the manufacturer’s instructions to carbonate. Gently release the pressure and pour into a chilled champagne flute. For the garnish, roll the melon peel around the bouquet of herbs and thread onto a cocktail pick and place across the top of the glass.