Heat the olive oil in a skillet; add mushrooms and onions and sauté 5 minutes. Salt and Pepper to taste. Stir 1 cup of the walnuts into the onion mixture and cook 3 minutes. Remove from heat.
Pound the chicken breast flat using a skillet. Salt and pepper both sides of the chicken breast. Stuff each breast with ¼ of the stuffing.
Beat the egg in a small bowl. Mix the corn flakes and walnuts in another bowl. Dip the chicken in the egg then the walnut/corn flake mix to coat. Place stuffed and coated chicken on a baking sheet and drizzle lightly with melted butter.
Bake at 375° F until done. Internal temperature should be 165° F.