Mix together cubed pineapple (plus any juice coming out of the fruit while cutting it), sugar, water, and cinnamon stick in a medium saucepan.
Cook over medium-high heat for about 30-35 minutes, stirring now and then, or until the pineapple becomes tender, lightly golden brown, and the liquid nearly evaporates.
Near the end of the cooking process, keep a close eye on the compote to prevent burning, since the liquid will have almost evaporated (leave about ¼ cup of liquid for use later in the recipe). Remove from heat and let cool completely.