Begin by preparing your puree and juice. Peel and de-seed your lychees (about 1 dozen lychee) and process in a blender. Remove the pulp to a fine mesh strainer or cheesecloth and extract as much juice as possible. Set aside. For the raspberry puree, simply blend the raspberries (approx 1 pint) until smooth, then pass through a fine mesh strainer to make sure there are no seeds in the puree (you will get enough juice for about 4 cocktails - store the juice in the fridge in an airtight container for up to 1 week).
In a shaker, combine the Empress 1908 Gin, Chambord, raspberry puree, lychee juice, and simple syrup with ice. Shake vigorously for 20 seconds. Pour the mixed cocktail into a tall glass filled three-quarters with crushed ice. Top the drink with Prosecco and serve.