Preheat oven to 375° F.
To make the syrup, in a heavy skillet, heat sugar over low heat, stirring constantly, until it melts and becomes dark brown. Slowly add boiling water. Stir until dissolved and boil to reduce to 3/4 cup.
To make the cake, in a medium bowl, cream butter and sugar. Add vanilla and eggs and beat well. In a separate bowl, mix together flour, baking powder and salt. Add dry ingredients to the egg mixture, alternately with the water, beating until smooth. Add 3 Tbsp of the burnt-sugar syrup and beat for 5 minutes at medium speed.
Pour into two 9-inch greased and wax paper-lined pans and bake for 20 minutes, or until a wooden pick inserted in the center comes out clean.
Cool 10 minutes in the pans, then turn onto cake racks and cool completely. Frost with Burnt-Sugar Frosting.
Combine egg whites, brown sugar, water, sugar syrup and salt and beat one minute to blend. Pour into the top of a double boiler and cook, beating constantly, until frosting forms stiff peaks, about 7 minutes. Don't over-cook. Remove the top of the double boiler to cool the surface.
Add vanilla and beat until frosting reaches spreading consistency, about 2 minutes. Frost cooled Burnt-Sugar Cake.Servings: One 9-inch two layer cake.