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Gather all ingredients. Preheat the oven to 350 degrees F (175 degrees C). Lightly grease a 9x5-inch loaf pan and line with parchment paper, leaving an overhang on the long sides.
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Whisk flour, baking soda, baking powder, and salt together in a large bowl.
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Blend cottage cheese in a blender or food processor until smooth; transfer to a bowl. Stir in melted butter or oil, mashed bananas, eggs, and brown sugar until well combined.
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Stir banana mixture into flour mixture just until combined; do not overmix.
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Scrape batter into the prepared pan and smooth the top.
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Bake in the preheated oven until a toothpick inserted in the center comes out clean, 60 to 65 minutes. Internal temperature of quick bread should be 205 to 210 degrees F (96 to 98 degrees C). If needed, cover bread with aluminum foil the last 20 minutes of baking to prevent over-browning.
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Let bread cool in the pan for 10 minutes. Lift out using the parchment overhang and transfer to a wire rack to cool completely, about 1 hour.