In a medium bowl, add the water, salt, and cornmeal and mix with your hands until well incorporated. Place a towel over the mixture and allow to sit for about 5 minutes.
Meanwhile, in a large skillet (I use a cast-iron skillet), add the oil and heat until it shimmers. Roughly divide the dough into 8 balls. Press the balls into 1/2-inch patties.
When the oil is hot, add the patties in batches spaced about 2 inches apart. Fry on the first side for about 4 to 5 minutes or until deeply golden on the bottom. Flip to the other side and continue to cook for another 4 minutes. Remove to a cooling rack over a sheet pan. Allow the arepas to cool completely. With a serrated knife, cut the arepas horizontally, creating two pieces for filling.
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