Chop the mushrooms very fine. Heat the oil in a sauté pan over medium heat. Add the mushrooms and toss and stir until they start to give off juices. Cook over high heat until all the liquid is reduced. Add the cream and cook until the mixture is thickened.
Mix the veal stock and Madeira in a small saucepan and reduce over high heat to ¼ cup. Turn the heat to low and whisk in 8 tablespoons of the butter, one tablespoon at a time. Do not let the sauce boil. Season with salt and pepper. Strain and keep warm in a double boiler over low heat.
Fill a shallow saucepan or frying pan with enough water to cover an egg. Bring to a bare simmer and add 1 teaspoon salt. Break the eggs one at a time directly into the water. Cook until the whites have congealed but the yolks are still runny. Remove the eggs carefully from the water and trim them. Blot them on towels to remove the excess water.
Reheat the mushroom mixture (duxelles) and stir in the remaining 1 tablespoon butter. Have ready 4 warm plates and arrange 3 slices of ham on each plate. Spoon the duxelles in the center of each plate. Put 2 eggs on top and pour over the sauce. Garnish with parsley.