In a thick-bottom pot combine milk, cinnamon and 1/2 cup of sugar and boil over medium heat until the milk has reduced to a quarter of the original volume.

Remove from heat and chill (after letting it cool down to room temperature).

In another pot combine pineapple with water, vanilla, lime peels, and the remaining sugar until the pineapple is really soft, with the consistency of a jam (add more water as it becomes necessary).

Let all the liquid evaporate and remove from the heat, then chill.

Mix the milk and pineapple (both should be chilled, or the milk will curdle). Keep and serve chilled.