So, I must say, this turned out to be so much better than I thought.
Preheat oven to 425 degrees. In a food processor, combine bread crumbs, walnuts, and Parmesan and season with salt and pepper. Process until fine breadcrumbs form.
Transfer to a shallow bowl. In another shallow bowl, beat egg white until frothy. Season chicken with salt and pepper. Dip each breast into egg white, letting excess drip off, and then into crumb mixture, pressing to stick to the chicken.
In a large nonstick skillet heat oil over medium heat. Add chicken and cook until lightly browned, about 1 to 3 minutes. Carefully transfer the chicken over to the roasting dish and place in the oven. Bake until chicken is golden brown and cooked through, 8 to 12 minutes.