To make the grilled pineapple juice, cut a whole pineapple lengthwise into eight pieces and grill until a medium char line develops. Remove the skin, juice the fruit and strain the solids.
To make the sage peppercorn syrup, bring all the ingredients to a slow boil and stir until the sugar is dissolved.
Remove from heat and allow to cool and fine strain into a container.
To assemble one drink, place the syrup, pineapple and lemon juices and ice into a cocktail shaker, shake then pour into a double-rocks glass (about a 6- to 8-ounce glass).
Fill with ice, top with ginger beer, lightly stir and garnish with mint sprig. Keep any unused juice and syrup in the fridge for the next round.