You can also cook the hash using a 7-cavity cast-iron biscuit pan. Preheat it in the oven for 15 minutes, then carefully press the carrot mixture equally into each of the molds, making a large well in the center of each. Brush with 1 tablespoon oil on top and bake until the carrots are set on top and deep golden brown, about 20 minutes. Then carefully crack an egg into each divot and bake until the egg whites are set and the yolks are still runny, about 8 minutes. Serve them from the pan!