To Poach eggs: bring 3 quarts water with vinegar to a boil. Break eggs into a bowl 1 at a time. Slide eggs into the boiling water one egg at a time and cook 3 minutes or until the egg white is completely cooked, yolk will be soft. Remove with slotted spoon and drain on paper towels.
Grill the ham slices a few minutes and place each half ham slice on each of the toasted English muffin halves. Place 1 slice of swiss cheese and 1 egg on top of each muffin half. Spoon a generous amount of the Hollandaise sauce and mushroom mixture over the muffins. Garnish and serve hot.
For Hollandaise sauce, in the top of a double boiler, beat egg yolk, evaporated milk, salt, and cayenne pepper until thick. Place over hot water. Beat lemon juice into egg mixture until thick and creamy. Remove double boiler from heat. Add margarine or butter, 1 teaspoon at a time. Beat until margarine or butter is melted and blended in. Add the sauteed mushrooms.