Cake: Combine cream cheese, 1 egg, and 1/4 c sugar in a medium mixing bowl; beat at high speed until smooth. Gradually add 3 tb milk and the next 3 ingredients, beating well. Set aside. Place chocolate squares in top of a dbl boiler; bring water to a boil. Reduce heat to low; cook until chocolate melts, stirring occasionally. Remove from heat and let cool. Cream 1/2 c butter; gradually add 2 c sugar, beating well at medium speed. Add 2 eggs, one at a time, beating well after each addition. Combine flour, baking powder, soda, and salt; stir well. Add flour mixture to creamed mixture alternately with 1 1/2 c milk, beginning and ending with flour mixture. Mix after each addition. Stir in melted chocolate and 1 ts vanilla. Spread half of chocolate batter in a greased and floured 13x9x2" baking pan. Spoon reserved cream cheese mixture evenly over chocolate batter; top with remaining half of chocolate batter. Bake at 350F for 55-60 minutes or until a wooden pick inserted in center comes out clean. Let cool completely in pan on a wire rack. Spread frosting over cake. Frosting: Combine chocolate and butter in top of a dbl boiler; bring water to a boil. Reduce heat to low; cook until chocolate and butter melt, stirring occasionally. Remove mixture from heat and let cool. Add powdered sugar and milk to chocolate mixture, beating at medium speed until smooth. Stir in vanilla.