Preheat the oven to 325°. In the same skillet, heat 1 1/2 tablespoons of the oil until shimmering. Add half of the hash mixture and flatten with a spatula. Cook over high heat for 2 minutes. Reduce the heat to moderately high and cook until the hash is richly browned on the bottom, about 2 minutes longer. Working in sections, turn the hash over and cook until browned on the other side, about 2 minutes. Transfer the hash to a large rimmed baking sheet and keep warm in the oven. Repeat with the remaining 1 1/2 tablespoons of oil and hash. Serve with fried eggs, hot sauce and ketchup.