Prepping pineapple: Peel and core the pineapple (you can use the peel and core to make Pera Piña or Guarapo). Mince in the food processor or by hand.
Cooking: Pour into a thick-bottomed pot, add water, sugar, and vanilla extract. Heat over medium heat until it reaches a gentle boil. Cover and boil over low heat until all the liquid has evaporated (90 min - 2 hrs approx.).
Storing: Remove from the heat and cool to room temperature before filling cake, or store in a tight container in the fridge for up to a week.
Video
Notes
If you use brown sugar (which I did in the video, and for some of the pictures), you get a deeper, more reddish color, and slightly less sweet jam. A reader in the comments report that she made it with canned pineapples, and although I would always suggest starting with the real thing, it appears that you can also get a decent enough result from tinned pineapple.