Heat the butter in a rather heavy 9 or 10 inch skillet, and sauté the onions, livers, mushrooms, and garlic 4 to 5 minutes over medium heat. Turn often.
Add the wine, lemon juice, and seasonings.
Grill the ham slices.
Fry the eggs in butter in small pans to keep them in rounds and more trim.
Arrange the ham on toast, top with an egg, spoon the sauce over all, and serve with a garnish of chopped parsley. Or make a layer of toast on a platter, top with ham, arrange eggs over all, and serve the sauce separately.