Preheat oven to 350°.
To prepare the brownies, coat the bottom of an 8-inch square baking pan with cooking spray (do not coat the sides of the pan).
Lightly spoon flour into dry measuring cups; level with a knife. Combine flour, baking powder, baking soda, and salt in a medium bowl. Combine granulated sugar and next 6 ingredients (granulated sugar through egg white); stir well with a whisk. Add to flour mixture; stir just until moist. Stir in cherries and walnuts. Spread batter in bottom of prepared pan.
Bake at 350° for 35 minutes or until a wooden pick inserted in the center of the brownies comes out almost clean. Cool on a wire rack.
To prepare the glaze, combine the powdered sugar, almond extract, and 1 3/4 teaspoons water in a small bowl. Drizzle the glaze over the brownies, and let stand for 15 minutes.