In a large bowl, combine the pre-cooked cornmeal and salt. Gradually add the warm water and 1 tbsp of oil, mixing with a spoon or your hands until a soft, pliable dough forms. It should hold together without being sticky. Let it rest for 5 minutes.
Divide the dough into 8 equal portions. Take one portion, flatten it in your palm, and place about 1-2 tablespoons of cheese in the center. Fold the edges over the cheese and roll into a smooth ball, then gently flatten into a disc about 1/2-inch thick and 3-4 inches wide. Ensure the cheese is fully sealed inside.
Heat about 1/4 inch of vegetable oil in a large skillet over medium heat. Once hot (a pinch of dough should sizzle), carefully add the arepas, working in batches to avoid crowding. Fry for 4-5 minutes per side, until deeply golden brown and crispy.
Transfer the fried arepas to a plate lined with paper towels to drain excess oil. Serve immediately while hot and the cheese is wonderfully melted.