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Preheat oven to 350F.
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Spray loaf pan with Pam.
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Beat butter in a large bowl with an electric mixer at medium speed until light and fluffy.
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Add sugar and brown sugar; beat well.
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Add egg, egg whites, and vanilla; beat until well blended.
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Add mashed banana; beat on high speed for 30 seconds.
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In a medium bowl, combine flour, baking soda, salt, and baking powder.
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Add flour mixture to butter mixture alternately with cream ending with flour mixture.
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Add walnuts to batter; mix well.
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Pour batter evenly into prepared loaf pan.
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Bake until browned and a toothpick inserted in the center comes out clean; about 1 hour and 15 minutes.
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Cool bread in the pan on a wire rack for 10 minutes.
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Remove bread from pan to cool completely on wire rack.
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This bread is best if wrapped in plastic wrap, left on the counter overnight to allow flavors to develop, and then served the next day.