For the cake, combine first seven ingredients (butter, sugar, egg, milk, flour, baking powder and salt). Pour batter into a greased 13" x 9" cake pan. Bake for 30 minutes or until cake tester inserted into center of cake comes out clean.
To make the sauce, combine the last five ingredients (sugar, boiling water, butter, flour and vanilla) in a saucepan over medium heat until sugar is dissolved and sauce thickens slightly. Remove from heat. The sauce will be thin.
Slice cake into 2-inch pieces and place each piece in a bowl to serve.
Pour a liberal amount of the sauce over each warm piece of cake and serve immediately. Do not pour sauce over entire cake, as it will become soggy.
Store left-over cake at room temperature for up to three days. Store sauce in refrigerator and warm in microwave when re-use desired.