In a large pitcher, combine most of the pineapple, the rest of the mint and a splash of the lime juice. (Reserve 6 to 8 pieces of pineapple for garnish.) Muddle to release the aromas of the mint and smash the pineapple. Add the rum and club soda and stir. Finish by adding more lime juice as you like it.
Pour into 6 to 8 ice-filled glasses and garnish each with a piece of grilled pineapple and a couple of tiny mint leaves.
Recipe note: For grilled pineapple, grill the pineapple for 3 minutes per side over medium high to high heat, just until browned and caramelized
It's a little time consuming to squeeze a cup of fresh lime juice but it's so worth it. Bottled lime juice has a chemical aftertaste that will take away from the fresh and bright flavors of your drink.