1. Mix corn flour and salt in a bowl. Stir in 2½ cups warm water and 1 tbsp. oil until dough forms; knead until smooth, 2–3 minutes. Divide dough into eight 4-oz. balls. Heat 2" oil in a 6-qt. saucepan until a deep-fry thermometer reads 325°. Flatten balls into 5" disks, about ¼" thick. Working in batches, fry, flipping once, until puffed, 3–4 minutes. Transfer to paper towels to drain.
2. Increase oil to 375°. Working with one arepa at a time, slice a 3" incision horizontally without cutting all the way through to make a pocket. Crack 1 egg into pocket; fry until egg is set, 2–3 minutes. Drain on paper towels; serve with hot sauce, if you like.