To make the pineapple compote: 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.
My compote was prepared on the large stove-top burner. If you are cooking on a smaller burner, it will take about double the time mentioned above to fully cook.
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 1/4 cup of liquid for use later in the recipe).