Bring the water and the papelón to a boil in a small to medium saucepan. Once it boils and the papelón has completely dissolved, lower the heat and simmer until it reaches the consistency of a syrup, about 30 minutes. Let cool completely.
Preheat oven to 350F.
While the papelón syrup is simmering, peel the plantains and slice them as if you were going to fry them.
Cover a tray with parchment paper and arrange the plantain slices on it.
Bake the plantains for 20-25 minutes until they look golden. They don't need to be flipped or overcooked. Take the plantains out of the oven and let them cool down.
Slice the cheese.
Using a silicone brush, brush the bottom of a 6-inch diameter cake pan with vegetable shortening, and cover the bottom with a parchment paper circle. Spray the bottom and sides of the pan with cake baking spray.
Arrange a layer of plantain slices on the bottom, spread about two tablespoons of papelón syrup, and then layer with cheese. Repeat until you end up with the last plantain layer.
In a bowl, beat the eggs with 5-6 tablespoons of syrup and a pinch of salt.
With a fine-point knife, make some incisions in the casserole.
Add the eggs and syrup mixture on top of the cake pan.
Put the cake pan on a tray and bake for 40 minutes or until the casserole is golden brown and has completely set.
Let cool for at least 15 minutes before unmolding.
To unmold, pass a knife or a small spatula along the sides of the pan, and with a not-very-wide spatula, unmold the cake and place it on the serving plate.