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Preheat oven to 350° F. Lightly butter a 9×5 loaf pan and set aside. (two smaller loaf pans work as well, but start watching for doneness in about 40 minutes)
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In a large mixing bowl, whisk together the flour, baking powder, baking soda, cinnamon, and salt.
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In the bowl of a stand mixer with paddle attachment, or in a large mixing bowl using an electric mixer, mix together the butter, granulated sugar, and brown sugar until light and fluffy (about 4-5 minutes). Mix in the vanilla, and the eggs, one at a time, making sure to mix well after each addition. Stop and scrape down the sides of the bowl, then add the mashed banana and mix until fully combined.
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Add the dry ingredients to the wet ingredients and mix until just combined, making sure not to overmix the batter. Then stir in the chopped walnuts.
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Scoop the batter into the prepared loaf pan and spread it around into one even layer.
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Bake at 350° F for 60-70 minutes or until a toothpick inserted into the center comes out clean. Tent with aluminum foil to prevent excess browning if needed.
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Remove from the oven and allow to cool in the loaf pan for 20 minutes. Carefully remove the bread from the loaf pan and transfer to a wire rack to finish cooling.