Lightly toast the rye and butter both sides of bread.
While it is toasting, cook the eggs over-easy with salt and pepper. (Eggs may also be scrambled or poached if desired)
Assemble the sandwiches, starting with the corned beef on top of the bottom bread, followed by the egg and swiss cheese.
Broil the open-faced sandwich for a few minutes, until the cheese melts.
Top with sauerkraut, sliced scallions and top half of bread.