In a large mixing bowl, combine 2 cups of masarepa flour, 2 teaspoons of salt, and 2 teaspoons of sugar. Add 2 tablespoons of unsalted butter and 1½ cups of freshly shredded mozzarella cheese. Mix well to incorporate the ingredients evenly.
Pour in ¼ cup of whole milk and slowly add 2½ cups of lukewarm water while continuously mixing the dough. Knead the dough until it becomes smooth and manageable, adding more water if necessary to achieve the right consistency.
Let the dough rest for about 5 minutes to allow the flavors to meld.
Divide the rested dough into 6 equal-sized portions and roll each portion into a ball. Flatten each ball into a disc shape, approximately ½ inch thick.
Heat a skillet over medium heat and spray it with 1 teaspoon of nonstick cooking spray. Place the arepas on the skillet and cook for about 5 minutes on each side, or until they develop a golden brown crust.
Let the arepas cool for a few minutes before serving. This brief cooling period allows the cheese inside to be perfectly melted and the crust to set.