Preheat the oven to 450°. In a pie plate, beat the eggs with the milk. Spread the flour and panko in 2 separate pie plates. Season the chicken all over with salt and pepper and dust in the flour. Dip the chicken in the egg mixture and then in the panko; press to help the crumbs adhere.
In a large skillet, heat the oil until shimmering. Add the chicken and fry over moderately high heat, turning once, until cooked through, about 7 minutes. Drain the chicken on paper towels, then transfer to a rimmed baking sheet. Top the chicken with the tomato sauce, Parmigiano, mozzarella and pepperoni.
Bake the chicken for about 15 minutes, until the cheese is melted and bubbling. Transfer the chicken to plates, sprinkle with the parsley and serve.
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