In a large bowl, combine the masarepa corn flour and salt until thoroughly combined. Make a well in the center and add the melted butter and water.
Gradually stir using a wooden spoon until no dry lumps remain. Adjust the consistency by adding more flour or water as needed; the dough is ready when it doesn't stick to the sides of the bowl or your fingers. Let it rest for about 5 minutes to hydrate.
Wet your hands, grab about 3 tablespoons of the dough, form a ball, and gently press it between your palms to flatten, forming about a ¼-inch thick patty. Pay attention to the edges, and smooth out any cracks. If using cheese, make a little well in the center of the dough ball before flattening. Place flattened disks on greased parchment paper and repeat with the remaining dough.
Heat a little oil in a large cast-iron or non-stick skillet over medium-high heat. Brown the arepas in batches, flipping once, until golden brown, for 5-8 minutes on each side. Finish them in a 350℉ (180℃) oven if you're concerned the outside will burn before the center cooks.
Transfer the arepas to a wire rack and let them cool. Split them and stuff them with the desired filling: shredded chicken, pork, chicken salad, or enjoy them as they are.