Preheat oven to 350. lightly grease an 11x7 inch baking pan with butter. For the base, in your standard mixer combine flour, sugar and butter and mix until dough comes together. Pat the dough gently into bottom of prepared pan.
Bake in center of oven until lightly golden, about 20 minutes. Place the base in the refigerator for 15 minutes to cool completely. Keep the oven on.
Meanwhile, prepare the topping; Melt the chocolate and butter in the top of a double boiler over simmering water. Cool slightly.
Beat the eggs, sugar, and baking powder together in a medium-size bowl with a whisk or fork. Add the chocolate mixture and stir vigorously with a whisk or fork until batter is blended. Spread chocolate mixture evenly over the base.
Bake the bars until the top rises and forms a very thin crust, about 20 minutes. The center will drop as it cools (can test middle with toothpick, it should come out alittle fudgy with some crumbs from cookie base) Cool completely on a rack. Cut the shortbread with a thin knife.