You need: ¼ pomegranate, 2 lychees, 2 parts cachaça, 1 part “Sophie’s syrup” (for that, boil 1 cup [250 ml] water, 1¼ cups [250 g] sugar, grated zest of 1 lemon and ½ orange, and seeds from 1 vanilla bean; strain and let cool, then stir in ⅓ cup [75 ml] rum), juice of 1 lemon, and a handful of ice cubes.
Peel the fruits and muddle them well with the other ingredients (except the ice) in the shaker.
Add the ice cubes and shake thoroughly.
Strain into a fancy glass. Alex cuts a snazzy lime curl to garnish it.