Preheat oven to 325 degrees F. Line 13 x 9-inch baking pan with foil.
Combine flour, baking powder and salt in large bowl; stir well.
MIcrowave chocolate and butter in large, microwave-safe bowl on HIGH (100%) power for 45 seconds; stir. Microwave an additional 30 seconds; stir until smooth and melted. Microwave at additional 15-second intervals as needed. Whisk in sugar. Add eggs one at a time, whisking after each addition. Whisk in vanilla extract. Gradually stir in flour mixture. Stir in half of chopped Butterfinger. Spoon into prepared pan.
Bake for 30 to 35 minutes or until wooden pick inserted in center comes out with moist crumbs attached. Cool on wire rack for 5 minutes; sprinkle top with remaining chopped Butterfinger. Cool completely before cutting into 2-inch squares.