Sauté ham, bread, and pepper in hot oil in a large skillet over medium heat 1 minute or until oil is absorbed. Reduce heat to low, and cook, stirring occasionally, 7 minutes or until bread toasts. Remove from heat.
Process white wine vinegar and next 4 ingredients in a blender until combined. With blender running, slowly add oil, processing until smooth. Slice lettuce lengthwise. Arrange lettuce, onion, and mushrooms on 4 serving plates.
Pour water to a depth of 3 inches into a large saucepan. Bring to a boil; reduce heat to a simmer. Add white vinegar. Break eggs, and slip into water, 1 at a time. Simmer 3 minutes or to desired degree of doneness. Remove eggs with a slotted spoon. Top each salad with egg, crouton mixture, and desired amount of dressing and Parmesan cheese.