For cake: In a bowl, cream butter until light. Gradually beat in sugar and vanilla. Beat in eggs, one at a time. Add salt and baking powder, mixing well.
Add unsifted flour alternately with milk, beginning and ending with flour. Pour the satiny batter into a greased and floured 13x9x2-inch baking pan. Bake in a preheated 350-degree oven for 25 minutes, or until a cake tester comes out clean. Let cake cool in pan on rack. Frost.
For frosting: In the upper half of a double boiler, over hot water, melt chocolate with butter. Stir in salt and vanilla. Remove from heat and blend in confectioner's sugar alternately with milk, beating smooth after each addition, until the consistency that will spread nicely. Spread over cooled cake.