Weigh or lightly spoon flour into dry measuring cups; level with a knife. Combine flour, baking soda, baking powder, and salt, stirring well with a whisk. Place butter and brown sugar in a large mixing bowl; beat with a mixer at high speed until well blended. Add eggs, 1 at a time, beating well after each addition. Beat in vanilla. Combine beer, sour cream, and 1/4 cup syrup, stirring well with a whisk. Beating at low speed, add flour mixture and beer mixture alternately to the butter mixture, beginning and ending with flour mixture; beat just until combined.
Scrape batter into a 9 x 5-inch metal loaf pan coated with baking spray. Bake at 350° for 43 minutes or until a wooden pick inserted in the center comes out with moist crumbs clinging. Cool 10 minutes in pan on a wire rack. Remove from pan; cool completely on wire rack.
Place powdered sugar in a small bowl. Add remaining 1 tablespoon syrup; stir until smooth. Drizzle glaze over cooled bread; let stand until set, if desired.