Put oil into 10-inch omelet pan or skillet with lid. Put pan on burner and heat over medium heat a little bit. Sprinkle a few drops of water into pan. The pan is hot enough when water sizzles and dances in the pan.
Add potatoes and onions to pan. Rub seasoning between fingers and sprinkle on potatoes and onions. Set timer for 8 minutes. With spoon, carefully stir potato mixture while it cooks. don’t stir all the time or potatoes will break into tiny pieces. Check potatoes when time is up. Keep cooking and stirring until potatoes are lightly browned.
Press back of spoon into potato mixture to make four holes, but don’t make holes so deep that pan shows through. Each one should be big enough around to hold 1 egg. One at a time, break eggs into mug or cup. Pour 1 egg into each hole in potato mixture.
Cover pan with lid. Set timer for 3 minutes. Cook until egg whites are set all over and yolks start to thicken and cloud over. The yolks don’t have to be hard. When 3 minutes are over, take of lid and check eggs. If eggs are still runny, put lid back on pan. Set timer for 1 minute. When 1 minute is over, take off lid and check eggs again. Sprinkle eggs with cheese when They’re done. Spoon 1 egg and one-quarter potato mixture onto each plate.
This recipe is a cross between poached and baked eggs. Instead of a pan full of water or a cup in the oven, the eggs cook in a nest of potatoes in a pan with a lid. The lid holds in steam to cook eggs all around, like in an oven.