Preheat the oven to 425°F (220°C). Place a wire rack on a baking sheet and set aside.
Slice each chicken breast horizontally to make two thin cutlets. Pound lightly between plastic wrap to an even thickness, about 1/2 inch.
Season both sides of the cutlets with 1 tsp kosher salt and 1/2 tsp black pepper.
Set up a dredging station with three shallow bowls: flour in the first, beaten eggs in the second, and breadcrumbs mixed with 1/4 cup grated Parmesan and dried oregano (if using) in the third.
Dredge each cutlet in flour, shaking off excess, dip into the beaten eggs, then coat evenly with the breadcrumb mixture. Place on the prepared rack.
Heat olive oil in a large skillet over medium heat. Fry the cutlets in batches until golden brown, about 2–3 minutes per side. Transfer browned cutlets back to the wire rack on the baking sheet.
Spoon about 1/4 cup marinara over each cutlet, then top with a slice of mozzarella (or shredded mozzarella) and a sprinkle of remaining Parmesan.
Bake in the preheated oven until the cheese is melted and bubbly and the chicken is cooked through, about 10–12 minutes.
Garnish with chopped parsley and serve immediately.
