Preheat oven to 350 degrees F. Line a 9x9x2-inch baking pan with foil, extending the foil over the edges of the pan. Set pan aside. For crust, in a medium bowl stir together 1 cup of the flour and the brown sugar. Using a pastry blender, cut in the 1/2 cup butter until mixture resembles coarse crumbs. Stir in 1/4 cup of the chocolate pieces. Press mixture evenly onto the bottom of the prepared pan. Bake for 8 minutes.
Meanwhile, in a large bowl stir together the remaining 3/4 cup flour, the granulated sugar, cocoa powder, baking powder, and salt. Add eggs, the 1/3 cup melted butter, and the vanilla; beat with a wooden spoon until smooth. Stir in the remaining 1/2 cup chocolate pieces. Carefully spread mixture over crust.
Bake for 40 minutes more. Cool in pan on a wire rack. Using the edges of the foil, lift the uncut brownies out of the pan. Cut into bars.