Line a baking sheet with waxed paper.
Season chicken breasts with salt and pepper.
Place flour on a plate.
Beat eggs and Dijon mustard to blend in a shallow baking dish.
Place 1 cup panko in another shallow baking dish, adding the remaining 1 cup panko, or more, to the dish as needed throughout the process.
Working with 1 chicken breast at a time, dredge in flour, shaking off excess, then dip into the egg mixture, turning to coat evenly; carefully coat with panko, pressing panko gently to adhere to the chicken.
Transfer chicken to the prepared baking sheet.