Pour 2 3/4 cups of hot water over flour and mix well with a wooden spoon. Stir in the melted butter. Cover dough with plastic wrap and let rest 15 minutes.
Divide the dough into 20 pieces, and form into balls. Place balls between 2 pieces of plastic and flatten with a heavy pot or skillet until they are about 3 1/2 inches in diameter and 1/4 inch thick, using your fingers to smooth out any cracks along the edges. Place arepas on a cookie sheet, covered with plastic wrap.
Heat a cast iron skillet on medium heat. Place 1/2 tablespoon butter or oil in the skillet. Place several arepas in the pan, leaving room so that you can turn them.
Cook arepas about 5 minutes on each side. The surface should dry and form a crust. They will brown slightly, but do not let them brown too much. They should look like an english muffin. If they are browning too fast, lower the heat. Add more butter or oil for subsequent batches as needed.
The arepas are done when they have formed a nice crust, but are still soft on the inside.