Pound each sheet of beef to 1/8th inch thick.
In a wide bowl, beat together 2 of the eggs, milk, parsley, salt, and pepper.
Place the breadcrumbs on a wide plate.
Coat a thin sheet of beef completely in the egg mixture, allowing the excess to drip off. Then cover in the breadcrumbs, pressing to make sure the beef is full coated. Repeat with remaining beef.
Allow the coated beef to rest in the refrigerator 30 minutes to overnight.
Pour oil into a large pan until 1/2 inch thick. Place over medium heat. Once fully heated, carefully add one of the coated beef slices. Fry until golden, about 5 minutes. Flip to cook the other side until golden. Transfer to a towel-lined plate and repeat with remaining beef.
While the beef is frying, lightly oil another pan and place over medium-high heat. Add two eggs and reduce heat to low. Fry just until set. Transfer two eggs over one slice of cooked Milanesa and serve immediately with fries.