How to Make It
In a saucepan, bring the pineapple, brown sugar and 4 cups of water to a boil. Simmer over moderately low heat, stirring, until the pineapple is very soft and the mixture is reduced to 2 1/2 cups, 40 minutes. Strain the mixture into a heatproof bowl, pressing on the solids; discard the solids. Let the syrup cool; you should have about 1 1/3 cups.
In a pitcher, muddle the pineapple and mint leaves. Stir in the rum, lime juice and 1 cup of the pineapple syrup. Pour into 8 glasses and add ice. Top with club soda and garnish with mint sprigs and lime wedges.