Pour the freshly squeezed lime juice through a fine mesh strainer to remove any small particles.

Add the strained lime juice, evaporated milk, condensed milk and vanilla to a blender or food processor and blend until the mixture is completely smooth.

Pour just enough of the mixture into the bottom of an eight-by-eight-inch baking dish to create a thin layer.

Cover the entire bottom of the dish with a single layer of cookies, breaking them to fill in gaps, if you need to.

Pour a layer of the milk mixture on top. You want enough to cover the cookies. Spread it out evenly.

Repeat with another layer of cookies and then another layer of the milk mixture, continuing until all the mixture is used up. Make sure the final layer is the milk mixture.

Sprinkle lime zest, to taste, on top, cover the dish with plastic wrap and refrigerate for at least two hours.

Slice the cake and serve it, and make sure to refrigerate the leftovers.