In a blender, combine the fresh or thawed corn kernels, whole milk, sugar, and salt. Blend until smooth.
Transfer the corn mixture to a mixing bowl and stir in the cornmeal and all-purpose flour until well combined. The batter should be thick but pourable.
Heat a non-stick skillet or griddle over medium heat and lightly grease with vegetable oil.
Pour about 1/4 cup of batter onto the skillet for each cachapa, spreading it out to form a pancake about 4-5 inches (10-12 cm) in diameter.
Cook for about 3-4 minutes on each side, or until golden brown and cooked through. Flip carefully as the batter can be delicate.
Remove the cachapas from the skillet and place them on a plate.
Spread a little butter on each cachapa while they are still warm.
Top with slices of cheese or fold the cachapas in half with cheese inside to melt slightly.
Enjoy your meal!