In medium bowl, stir together Masarepa and 1 tsp. salt. Add 2 ½ cups lukewarm water. Stir until combined; let sit 5 minutes. Using wet hand, knead dough until smooth. Divide dough into 9 portions. Form dough into 8 small balls, reserving remaining portion of dough to patch up holes later. Using press, or palm of hands, flatten balls to ¼” thickness.
Meanwhile, fill heavy pot with oil to depth of 1½”. Heat oil until it registers 325˚F on deep-fry thermometer. Add arepas to oil. Cook until arepas puff, about 5 minutes; transfer to paper towel-lined plates to drain and cool.
Using knife, make 2” incision into one side of arepa to form pocket. Crack egg into espresso-size cup or small ramekin. Carefully slip egg into pocket. Using reserved portion of raw dough, seal together split end.
Heat oil to 350˚Add egg-filled arepas to oil. Cook until light golden brown on all sides, about 5 minutes for soft-set yolks. transfer to paper towel-lined plates to drain. Season with remaining salt.
Moist cornmeal dough is the key to creating smooth arepas that stay crack-free as they cook (and, in turn, prevent the eggs from leaking out). To keep the dough moist, cover with damp kitchen towel before frying.