Peel and core the pineapple. Cut into chunks, and reserve 6 pieces. Purée the rest of the pineapple in a food processor or blender, then set aside.
In a large pitcher, add mint, arugula, limes, and brown sugar.
Muddle the leaves, limes and sugar together using a spoon or muddler.
Add puréed pineapple, pineapple juice, and rum to the pitcher. Top with a good splash of club soda.
Pour over ice, and garnish each glass with a pineapple chunk, mint, and more lime wedges.