Pound flat each breast between 2 sheets of plastic wrap. Top each with ham and chicken. Moisten edges with egg to hold together. Roll breasts in flour and shake off excess.
Melt butter in shallow pan. Saute fillets for 10-12 minutes. Turn and continue to sauté for 5 minutes on each side. Remove and keep warm in oven. To butter in pan, add shallots, mushrooms and wine. Cook until reduced by half. Add cream and cook until fairly thick. Seaon and pour over chicken.