Preheat the oven to 350°. Butter and flour two 8-by-1 1/2-inch round cake pans. Line the bottoms with wax paper. In a medium bowl, sift together the flour, baking powder, baking soda and salt; set aside

In a medium saucepan, combine the sugar with 2 cups of water. Bring to a boil over high heat and stir until the sugar dissolves; then pour into a large bowl. Add the chocolate and butter and let sit, stirring occasionally, until melted and slightly cooled. Stir in the vanilla

Beat the eggs into the chocolate mixture at medium speed until combined. Add the dry ingredients all at once and beat at medium speed until smooth. Divide the batter evenly between the prepared pans and bake for about 25 minutes, or until the top springs back when pressed lightly and a cake tester comes out clean. Cool the cakes in their pans for about 25 minutes, then invert onto a rack to cool completely

Set one cake, right-side up, on a serving platter. Using a metal spatula, spread one-third of the Chocolate Frosting evenly over the cake. Top with the second cake and frost the top and sides with the remaining frosting