Preheat the oven to 425°F. Line a baking sheet with parchment paper or foil.
In a medium shallow bowl, stir together the breadcrumbs and Parmesan cheese. In a second shallow bowl, whisk together the flour with 1/4 teaspoon black pepper. In a third shallow bowl, whisk together the eggs and Dijon mustard.
Dredge the chicken breasts in the flour then dip them in the egg wash and then into the breadcrumb mixture, pressing it onto all sides.
Coat the bottom of a large skillet set over medium heat with a liberal amount of oil. In batches, sear the chicken breasts on both sides until golden brown then transfer them onto prepared baking sheet, spacing them at least 2 inches apart. (See Kelly’s Note.)
Bake the chicken until it is cooked through and reaches an internal temperature of 165°F.
Remove the chicken from the oven and serve.