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Preheat the oven to 375 degrees F (190 degrees C). Line a 9x9-inch baking pan with parchment paper.
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Stir together rolled oats, baking powder, cinnamon, and salt in a bowl; set aside.
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Mash bananas in a large bowl until smooth. Whisk in milk, eggs, maple syrup, brown sugar, and vanilla extract until well combined.
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Add oat mixture to banana mixture and stir until evenly blended. Pour batter into the prepared pan.
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Bake in the preheated oven until golden brown and set, 35 to 40 minutes.
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Transfer the pan to a wire rack and cool completely, about 30 minutes.
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Cut into 9 bars. Serve and enjoy!