Whisk the cornstarch, sugar, and half of the flour, then add 1 cup of milk and combine. Set aside.
Heat the remaining milk over medium-low heat in a large saucepan until it starts to bubble. Remove from heat and add the cinnamon stick, lemon peel, and vanilla. Mix and let sit for 5 minutes.
Gradually strain the milk from the saucepan into the mixture from the first step, and stir until combined. Return the mixture to the saucepan and heat over medium-low heat, stirring constantly, until the mixture thickens considerably. This will take about 15 minutes.
Oil a large baking dish and pour the mixture into it. It should be about ¾ inch (2 cm) deep. Cover with plastic wrap or wax paper so that it's resting on the surface of the mixture, and refrigerate for a minimum of 4 hours, or overnight if possible, until it has solidified.
Turn the cooled mixture out of the pan and cut into small squares. Dip each piece in beaten egg and then in flour to form a light coating.
Heat the olive oil in a frying pan over medium heat, at a depth of about ¼ inch (½ cm). Fry the cubes in the oil for about one minute on each side, until the coating turns golden. Let the leche frita drain on a paper towel, then roll in sugar and cinnamon.
Serve fresh or at room temperature, ideally with ice cream.