Place first the milk, and then the corn, eggs, sugar, and salt in a blender and blend until well mixed. The mixture will be thick, so scrape down the sides as needed for an even blend.
Add the butter and cornmeal and blend until just incorporated.
Transfer the mixture to a mixing bowl, cover, and let it rest in the refrigerator for 20-30 minutes.
Melt a little butter in a nonstick frying pan on medium-low.
Spoon ¼ of the batter into the pan and flatten it with the back of a ladle, moving the ladle in a circular motion to form an even round shape.
Cook for 8-10 minutes and then flip it when holes form on the upper surface, the underside is browned, and the underside comes away from the pan easily with a spatula. Flip it very carefully so it doesn't break.
Let the other side cook for 3-4 minutes until browned.
When the cachapa is almost finished cooking, spread a little butter on the surface until it melts.
Arrange ¼ of the cheese slices on half of the cachapa, and then carefully fold it in half with a spatula and press the top down lightly to adhere it to the cheese.
Remove the cachapa from the pan and repeat frying and filling for 3 more cachapas.