Start by preparing simple syrup.
In a small pan over medium heat bring the water to simmer, add the sugar and let simmer until reduced by half. Chill the syrup completely before using.
Peel, core and slice the pineapple. Blend the pieces in a blender and then strain the resulting fruit puree to capture and remove the fibers.
Place the strained pineapple puree in a bowl (if using only one pineapple add the pineapple juice) and add the chilled simple syrup and the lime juice.
If making pineapple sherbet, add the milk.
If making the IPA pineapple sorbet version, add the IPA.
Mix very well, refrigerate briefly to chill and just prior to adding to the bowl of your ice cream maker mix very well again.
Use the ice cream machine as directed in the product instructions.
Serve the sherbet/sorbet immediately with a slice of fresh pineapple as garnish or place in an airtight container and freeze for later use.