Mix the precooked cornmeal, cheese, salt. Add the water and stir until combined, getting rid of any lumps and adding just enough extra water, as needed, to moisten the mararepa. Cover and let the mixture rest for 10-15 minutes.
Using your hands, divide the dough into 4 equal pieces. Roll each piece into a ball and flatten gently to create a disk, about 3/4-inch thick. (The arepa will be similar in size to an English muffin. You want just enough thickness to be able to slice it in half after cooking. If the dough isn’t totally smooth when shaping, wet your hands and smooth out any cracks.)
Heat the butter and oil in a 9- to 10-inch heavy skillet over medium heat. (Cast iron works well. It’s fine to use a bigger skillet than stated; you may simply need a little more butter and oil to lightly coat the surface.) Add the arepas and cook for 5 minutes on the first side. Flip and cook for 3-5 minutes on the second side. Try not to disturb them too much while cooking. Peek underneath towards the end of the cooking time to check for patches of golden color. The arepas should have a slightly crispy exterior without being overly brown. This way, the insides will be cooked but tender with a bit of moisture.
Cut the arepas in half and stuff with your filling of choice***…or spread the halves with a little butter and serve instead of a roll or biscuit as a side to soup, salad, or your morning eggs. Arepas are delicious served hot but can also be enjoyed at room temperature.