In the medium bowl, toss together the arepa flour, cheese, and salt, then stir in the water until well mixed. Let the mixture stand until enough water is absorbed for a soft dough to form, about 2 to 3 minutes.
Divide the dough into 6 pieces. Form the pieces into balls and flatten between your palms, gently pressing to form a 1/4-inch-thick patties, then gently press around side to eliminate cracks. Place the shaped arepas on wax paper.
Heat oil in the cast-iron skillet over medium heat until it shimmers, then fry arepas in 2 batches, turning over once, until deep golden in patches, about 8 to 10 minutes total per batch. Drain on paper towels.
Put all the ingredients in a food processor or blender and process until slightly blended, but still a bit chunky. Dollop on top of the cooked arepas.