How to Make It
In a medium bowl, stir together the masarepa, 1 teaspoon salt, sugar, and 1 cup hot water to form a stiff dough. Cover with a damp cloth and let stand for 20 minutes.
Pour oil into a large Dutch oven to a depth of 2 inches and heat to 375°F.
Divide dough into 4 equal pieces, and roll each into a ball. Gently press each between 2 sheets of wax paper to form 4-inch-wide rounds (about 1/3 inch thick). If edges crack, smooth and press edges together with hands.
Fry the arepas in the heated oil until light golden and slightly puffed, about 3 minutes. Re- move and drain on paper towels. Cool to room temperature, about 10 minutes. Keep oil hot.
Using a small knife, cut a 2-inch slit along one edge of the arepa. Using a spoon, open a small pouch in the arepa without widening the slit. Crack 1 egg into a small cup, add a pinch of salt, then pour into arepa. Gently press the arepa closed, then carefully slip it into the hot oil. Fry until egg white is set and arepa is crispy, about 3 minutes. Remove with a slotted spoon and drain on paper towels. Repeat with remaining arepas, eggs, and salt. Serve with avocado slices, cheese, hot sauce, and cilantro.