Defrost the corn by placing it in a colander and rinsing it under cold water. Drain well and set aside for about 10 minutes.
Place the defrosted corn in a blender and puree with the milk, sugar, salt, and pepper, to taste. Transfer the mixture to a medium bowl and stir in the cornmeal to make a thick pancake-like batter.
Melt 1 tablespoon of butter in a nonstick skillet or griddle over medium heat.
Add 3 tablespoons of the arepa batter to skillet, using the bottom of a spoon to flatten. Spread the batter into a 3 to 4-inch circle. Cook arepas for about 8 minutes or until the bottom is golden brown. Flip arepa and cook for an additional 4 to 5 minutes until crisp. Add more butter from the remaining 3 tablespoons to the skillet between batches when necessary.
With a 3-inch cookie cutter, cut out circles from the cooked arepas while still warm. Lay 1 slice mozzarella cheese over cut out arepa. Top with another cut out arepa to create a sandwich.