To a large deep and wide pot, preferably a caldero, add your milk and mix together the sugar, cinnamon, and lime peels. Put heat on medium low and let the milk mixture cook for about an hour, stirring only once or twice during that hours period.
After an hour, the milk should be a beautiful caramel color. If there is still a lot of liquid, continue cooking, stirring occasionally until the consistency is that of a ragu or picadillo, where there's still a little bit of liquid, but not much at all.
Transfer dulce de leche cortada into a large class container or bowl.
Serve hot or cold, refrigerate any leftovers.
Notes
If you're using fresh milk, add about 2 tablespoons of the juice of the lime or white vinegar, and let it sit about 10 minutes, or until the milk splits and becomes curdled.For the lime peel, the amount to be used is about a ⅙ or ¼ of the limes peel for a gallon worth of milk.