Stir the warm water, salt, and melted butter together in a large bowl. Gradually add the cornmeal, mixing with your fingers until a soft dough forms.
Rest the dough for 5 minutes. Divide it into 4 balls and flatten each into a 1/2-inch-thick disk. Smooth any cracks with damp fingers.
Cook the Arepas:
Heat the oil in a nonstick skillet or griddle over medium heat. Cook the arepas for 5 to 7 minutes per side, until golden and firm.
Lower the heat, cover, and cook for 3 to 5 minutes more so the centers finish gently.
Fill and Serve:
Carefully split each arepa almost all the way through. Fill with the cheese and return to the skillet for 1 to 2 minutes per side, until the cheese melts.
Serve hot with avocado and cilantro.
Notes
Use masarepa or another pre-cooked cornmeal made for arepas; regular corn flour will not produce the same texture.
Cheese that melts well, such as mozzarella, queso blanco, or Oaxaca cheese, works best for filling.
Keep the cooked arepas warm under a towel while finishing the batch.