Position a rack in the center of the oven and preheat to 350 degrees F.
Stir together 2 1/2 cups lukewarm water and 1 1/2 teaspoons salt in a large bowl. Gradually add the corn meal into the water, using your fingers to stir and combine, until a soft and moist dough forms.
Divide the dough into 8 golf ball-size balls and pat each into a patty about 5-inches wide and 1/4-inch-thick.
Put a cube of mozzarella in the center of each patty. Fold the dough over the cheese, making sure the cheese is completely covered and sealed. Pat it back down until 3-inches wide and 1/2-inch-thick (see Cook's Note).
Heat the oil in a large skillet over medium-low heat until shimmering. Working in batches, cook the corn patties, until golden brown, about 5 minutes per side (making sure the oil is hot for each batch). Transfer to a cooling rack set on a rimmed baking sheet and bake until the edges are crisp and golden, about 10 minutes.
You can skip the cheese and make plain arepas to stuff with your favorite fillings, such as shredded beef or pork or avocado and beans. Form patties that are 3-inches wide and 1/2-inch-thick and cook according to directions. When the arepas are cool enough to handle, use a thin serrated knife to slice a third of the way through each arepa. Then use the knife tip to cut open the center of each to form a pocket, taking care to keep the sides intact. Wipe down the knife between cuts to remove any sticky cornmeal. Then stuff with the fillings of your choice.
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