Heat oven to 375°F. In medium saucepan, melt butter; stir in flour, salt and pepper until well blended. Add milk all at once. Cook about 1 minute until thickened, stirring occasionally. Stir in chicken, cheese and mushrooms; set aside.
Separate biscuit dough into 8 biscuits. Roll or pat each into 5-inch circle. Place about 1/3 cup chicken mixture on each biscuit circle. Wrap dough around chicken mixture, pressing edges to seal.
Dip rolls in egg, then coat with crushed cornflakes. Place on ungreased cookie sheet. Bake at 375°F. for 20 to 25 minutes until golden brown.