Lightly beat eggs in a small bowl. Soak the chicken pieces in the egg for at least 30 minutes. Meanwhile, melt the butter in a large frypan and add the mushrooms. Cook and stir the sliced mushrooms until softened.
Remove the chicken from the egg mixture. Roll the chicken pieces in bread crumbs and set aside. Heat a small amount of oil in a large frypan over medium-high. Place the chicken pieces in the pan and brown on all sides. Brown the pieces in batches if necessary.
Place the browned chicken pieces in a 20x30cm glass baking dish. Cover the chicken with the sauteed mushrooms. Pour the wine into the baking dish then cover the mixture with the sliced cheese.
Bake in preheated oven for 30 to 40 minutes or until the chicken is cooked through.