Put the pineapple, mint leaves, and lime juice in the bottom of a tall glass.
Use a muddle or the end of a spoon and crush the ingredients together, smashing the pineapple.
Fill the same glass with ice with the pineapple mixture still in it.
Pour the rum over the ice followed by the simple syrup.
Top off the glass with club soda and stir. Garnish with more limes, mint, and pineapple as desired.
Turn this drink into a mocktail (without liquor) by omitting the rum and replacing with more club soda, tonic, or lemon lime soda.You can use a sweeter mix in if preferred (instead of club soda) such as tonic or lemon lime soda.These can be made in a batch in advance by combining all ingredients except the club soda together. Top off each glass as poured with the club soda.To make simple syrup, combine 1/2 cup water and 1/2 cup sugar over medium heat in a small pot. Simmer until sugar is dissolved and let cool before using. Keeps in the refrigerator up to a month and makes about 1 cup (16 Tablespoons).