Preheat oven to 350*F. Lightly grease an 11"x7" baking pan with butter.
For base, process flour and sugar in food processor about 15 seconds. Add the butter and process until the dough comes togetther, 20-30 seconds.
Pat the dough gently over the bottom o0f prepared pan. Bake on center oven rack until it is lightly golden, about 20 minutes. Place the base in the refrigerator 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. Add the chocolate mixture and stir vigorously with the whisk until the batter is blended. Spread the cohocoate 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. Check with toothpick inserted in the middle. It may come out with a fudgy, crumbly batter on it, but it should not be liquidy. Cool completely on wire rack. Cut the shortbread with a thin knife. Enjoy!