The arepa de huevo is a sandwich that cooks its filling inside its own bread in a single step. A corn dough is shaped, partly fried until it puffs and forms a hollow, then split, a raw egg is slipped into the pocket, and the whole thing goes back into the oil so the egg sets sealed inside the dough. There is no assembly in the usual sense and no second slice. The bread and the filling are fried together, and the seal of the corn shell around the egg is the entire structural idea. Get the seal wrong and the egg bleeds into the oil; get it right and you have a self-contained sandwich with a custardy center and a crisp shell.
The craft is in the dough and the two fries. The dough is precooked corn flour worked with water and salt into something pliable enough to shape and tight enough to inflate when it hits hot oil, which is what creates the hollow the egg needs. The first fry is shorter and is about geometry, not color: it has to puff the disc and firm the outside without cooking it through, so there is a pocket to open and time left for a second fry. The egg goes in raw, sometimes with a little seasoned ground meat tucked alongside it, and the dough is pressed shut so the heat of the second fry cooks the egg from a liquid into a barely-set, soft interior while the shell crisps and deepens. Timing is the whole discipline: too long and the yolk goes chalky and the point is lost, too short and the white is raw. It is street and breakfast food, fried to order at a cart or a counter and eaten hot in the hand within minutes, because the contrast between the crackling corn exterior and the soft egg inside collapses as it sits.
The variants stay close to what goes in beside the egg. A plain egg, an egg with seasoned ground beef, an egg with both meat and a spoon of the cook's hot sauce on the side. It belongs to the broad family of folded and filled flexible-dough sandwiches that travel with immigrant communities, and those relatives deserve their own articles rather than being crowded in here.