Heat oven to 350 degrees Fahrenheit.
Beat 2 of the eggs in a medium bowl, add the potatoes, 2/3 cup cheese, and meat (add spices now or sprinkle over eggs or cheese, later), mix well.
Prepare 4 custard cups, ramekins or large muffin tin cups with nonstick spray or by greasing. If you don't have cups large enough, use a round cake pan or similar size casserole.
Fill cups halfway with potato/meat mixture, then form a well in the center large enough to accommodate a whole egg, pressing the mixture up to the top edge of the cup. (For one pan, place all the mixture in the pan, then make 4 wells for the eggs.).
Bake in oven for 10 to 15 minutes (until barely starting to brown), then take out of oven, break each of the 4 eggs into a cup one at a time, and then place each into one well apiece (sprinkle desired spices/parsley over egg, if you like, or put over cheese, next step). Return to oven for 5 minutes (just until white is cooked, or longer for medium or firm yolks), then sprinkle remaining cheese over the tops (could sprinkle with parsley and/or spices now, if desired/not used before) and return to oven for another 2 to 4 minutes, until cheese is melted.
Serve in or out of the individual cups on plates, or use a pancake turner or pie server to plate individual servings if using a single pan.