Grill pineapple for 3 minutes per side over medium high to high heat, just until browned and caramelized.
In a large pitcher, combine most of the pineapple, the mint and a splash of lime juice. (Reserve 6-8 pieces of pineapple for garnishes on the glasses). Muddle to release the aromas of the mint and smash the pineapple. Add the simple syrup (to taste), the rest of the lime juice, the rum and the club soda and stir.
Pour into ice-filled glasses and garnish each with a piece of grilled pineapple.