I saw this idea on the internet once and wanted to try it. My eggs turned out absolutely perfect -- which is surprising cause I cannot cook eggs for the life of me. I did what Alton Brown said to do: crack the eggs into a small bowl first, tilt the pan and add the egg into the pan. It will stay snuggled up into the corner and wouldn't spread. The problem is, the egg is gonna cook into a moon shape, so before the whites completely set, flatten the pan and drag out the egg whites with a spatula into a round shape.
For the hash browns, grate one russet potato and soak it in water. Rinse it in running water until the water runs clear. Squeeze out every drop of the remaining water and pat dry with some paper towel. Season with Salt and pepper and start frying it.
You don't need to shape it right at the start. Cook the potato first until it becomes mushy and begins to stick to each other. Then you can shape it into a nice round shape and turn up the heat to get the nice crispy sides. You may need a little extra oil for it to crisp up.
Top each potato cake with an egg and some chopped chives and serve!