In a large bowl, cream shortening and sugar until light and fluffy. Add egg, then egg white, beating well after each addition. Stir in vanilla. Combine the flour, cocoa, baking soda and salt; add to the creamed mixture alternately with milk, beating well after each addition. Stir in water until smooth. Pour into a greased and floured 6-in. round baking pan.
Bake at 350° for 40-45 minutes or until a toothpick inserted in the center comes out clean. Cool for 10 minutes before removing from pan to a wire rack to cool completely.
In a small saucepan over low heat, combine the sugar, cream and butter. Bring to a boil; cook and stir for 2 minutes. Remove from the heat; stir in marshmallows and chocolate chips until smooth. Spread frosting over top and sides of cake.