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Preheat oven to 350 degrees.
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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.
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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.
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Slice cake into 2-inch pieces and place each piece in a bowl to serve.
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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.
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Store left-over cake at room temperature for up to three days. Store sauce in refrigerator and warm in microwave when re-use desired.