Make watermelon juice: Place watermelon pieces in a blender or food processor and blend until smooth. Strain through a fine mesh sieve.
Make ginger juice: Place minced ginger in a blender or food processor, add 1/4 cup of cold water. Blend until smooth then strain through a fine mesh sieve.
Make the cocktail: Fill a wine glass with ice cubes, add Prosecco, Aperol, club soda and 2 oz of your watermelon juice. Top with a splash of the ginger juice and stir. Garnish with a slice of watermelon. Cheers!