Fry onions or shallots and mushrooms in butter until the onions are to the sweet caramelized point and the mushrooms are browned. Set aside.
Toast a piece (or two) of rye bread. Set aside.
Butter up the pan again and place your egg molds at the bottom. Crack an egg into each and put the lid on the pan. Cook for 2-3 minutes, or until the white has set.
Remove eggs from heat, take them out of the molds, and place them on top of the rye bread. Sprinkle grated cheddar cheese on top of the eggs, then place caramelized onions and mushrooms on top. Eat and enjoy!