Pound the cutlets to just under 1/4-inch (remember to look for steaks with little fat and no sinew, which makes the milanesa curl up as you cook it).
Whisk together the eggs, parsley, milk and garlic. Add salt and pepper to taste.
Leave the cutlets soaking for 30 minutes to one hour in the fridge. The more time the better.
Preheat the oven to 400 degrees F. Lightly cover a baking tray with oil and heat it up in the oven.
Spread the breadcrumbs out in a shallow bowl and one by one place the cutlets into the crumbs, turning and pressing firmly until they are well covered.
Add the milanesas and cook for about 5 minutes, or until the bottom is golden brown.
Turn over the milanesas and spread on a layer of tomato sauce, a piece of ham, if using, and three pieces of cheese. Sprinkle with oregano.
By the time the cheese has melted the bottom should be nicely browned, 3 to 5 minutes more. For best results, use the broiler for half of the suggested cooking time in this step to melt the cheese.