Preheat oven to 375°
Place 4 slices of sliced bread on a sheet pan, bottom side oiled or buttered. Sprinkle just a little cheese (about a tablespoon) on each slice of bread, then evenly distribute ham pieces, about 1/2 Cup per slice. Top with remaining cheese and put in oven for about 10 minutes, or until cheese is melty and bubbling.
Meanwhile, use a large glass or biscuit cutter to cut a hole in the remaining 4 slices of bread. Reserve bread discs for another use. (You may consider toasting and use to dip in the egg yolk).
Butter or oil both sides of the bread frame, taking care not to break it (but if you do, that's ok). Toast one side until golden brown in a large skillet or griddle over medium low heat, then flip; about 3-5 minutes.
Crack one egg into each bread frame and cover the pan to steam the eggs. When the whites look set and opaque on the top, turn off heat and sprinkle with salt, pepper and herbs.
Remove ham and cheese slices from the oven and top with One-Eyed egg slices. Serve hot, with a small green salad if desired.