Preheat oven to 375°. Chop mushrooms very fine. Melt butter in a large skillet and add mushrooms. Cook until mushrooms turn dark, about 6-8 minutes. Add 3/4 cup of the breadcrumbs, salt, pepper, and nutmeg. Mix well.
Meanwhile halve each chicken breast horizontally and pound flat.
Place 1/8th of the mushroom mixture on each of the flattened chicken breasts, roll tightly, seal the ends, and place seam side down in a glass 9 x 13 baking dish. Sprinkle the remaining breadcrumbs over the chicken, then pour cream over. Bake uncovered for 30-40 minutes or until done. Test the meat to ensure it is fully cooked.