Separate 4 of the yolks from whites.
In a mixing bowl, combine the egg whites and four whole eggs. Beat well.
Add 1 tablespoon oil to a skillet on medium high heat.
Add in the corned beef and char on all sides. Remove from pan and set aside.
Add in the rye bread and crisp on all sides.
Add back in the corned beef and add in the milk.
After the milk is absorbed, add in the second tablespoon of oil.
Pour in the beaten eggs.
Add the salt and pepper and 3 broken slices of the cheese.
Cook for two minutes on stovetop.
Place in a 350 degree oven and back for 15 minutes until it just sets.
Remove from the oven and top with the remaining cheese.
Place back in the oven and cook for 3 more minutes.
Serve and enjoy.