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 and next 5 ingredients (through 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.