Combine masa harina, flour, and salt in a bowl. Stir water and egg into the masa mixture; add melted shortening and mix well to form dough.
Gently knead dough until moist but retains shape; transfer to a bowl, cover bowl with plastic wrap, and refrigerate for 1 hour.
Divide chilled dough into 15 portions. Roll 1 portion of dough into a ball, while keeping remaining dough covered to prevent it from drying. On a lightly floured work surface, pat ball into a 3-inch round. Pinch along the edges of the round to make a ridge. Repeat with remaining dough portions.
Pour enough oil into a skillet to be about 1/2-inch deep; heat to 365 degrees F (185 degrees C). Fry a couple shells in hot oil at a time until crisp, 1 to 2 minutes per side. Remove sopes from oil using a slotted spoon to a plate lined with paper towel. Add more oil as needed and reheat between batches.
