To Make Mushroom Filling: Melt 1/4 cup butter in a small skillet over medium heat. Add mushrooms, salt and pepper and saute together, stirring, until mushrooms are dark. Remove skillet from heat; stir in nutmeg and 3/4 cup bread crumbs.
Spoon mushroom mixture onto the end of each chicken breast, roll up and fasten with toothpicks. Place seam side down in a lightly greased 9x13 inch baking dish. Brush 1/8 cup melted butter over breasts, then sprinkle with remaining 1/4 cup bread crumbs. Pour cream over all.
Bake uncovered at 350 degrees F (175 degrees C) for 30 minutes or until chicken is cooked through and no longer pink.