Stir together the bananas, granulated sugar, Worcestershire sauce, oil, brown sugar and eggs in a medium bowl. Let rest at room temperature 30 minutes.
Meanwhile, preheat the oven to 350 degrees F. Butter the bottom and sides of a 9-by-5-inch loaf pan and dust with 2 tablespoons flour.
Whisk together the walnuts, baking powder, cinnamon and remaining 1 1/2 cups flour in a large bowl and toss to coat the walnuts. Add the wet ingredients to the dry ingredients and stir to combine.
Pour the batter into the prepared loaf pan and bake until the top is golden and a toothpick inserted in the center comes out clean, 50 minutes to 1 hour. Let cool a bit before removing from pan, slicing and serving.