Place a rack in the center of the oven and preheat oven to 350 degrees F. Grease an 8-inch square baking sheet. Line with parchment paper, leaving two flaps hanging over the edges of the pan. Grease and flour the parchment paper. Set aside.
In a small bowl, whisk together flour, baking powder, baking soda, ginger, and salt. Add all at once to the butter and sugar mixture. Stir until just incorporated. Mixture will be fairly thick. Fold in ginger, chocolate and walnuts, reserving some of each to top the brownies before baking.
Spread batter into prepared pan. Top with remaining ginger, chocolate, and walnuts. Bake for 20 to 27 minutes, or until a skewer inserted in the center of the brownies comes out clean. Brownies will be golden brown.