Preheat oven to 350°.
Combine banana, 1/2 cup brown sugar, 5 tablespoons butter, and 3 tablespoons cognac in a nonstick skillet. Cook over medium heat until mixture begins to bubble. Remove from heat; cool. Place banana mixture in a large bowl. Add yogurt, remaining 1/2 cup brown sugar, and eggs. Beat with a mixer at medium speed.
Weigh or lightly spoon flour into dry measuring cups; level with a knife. Combine flour, ground flax, baking soda, salt, cinnamon and allspice in a small bowl. Add flour mixture to banana mixture; beat just until blended. Pour batter into a 9 x 5-inch loaf pan coated with cooking spray. Bake at 350° for 1 hour or until a wooden pick inserted in center comes out clean. Remove from oven; cool 10 minutes in pan on a wire rack. Remove bread from pan; place on wire rack.
Combine remaining 1 tablespoon melted butter, remaining 1 tablespoon cognac, and powdered sugar; stir until well blended. Drizzle over the warm bread.