Preheat oven to 375 degrees. Whisk together flours, bran, baking soda, salt, and cinnamon in a medium bowl; set aside.
Put butter and brown sugar into the bowl of an electric mixer fitted with the paddle attachment. Mix on medium speed until pale and fluffy, about 3 minutes. Add eggs, 1 at a time, mixing until combined after each addition. Add bananas, applesauce, and vanilla; mix until combined. Reduce speed to low. Add flour mixture; mix until just combined. Stir in 3/4 cup muesli and the blueberries.
Line 10 cups of a standard (12-cup) muffin tin with paper liners. Divide batter among cups, filling to rims. Sprinkle tops with remaining 1/2 cup muesli. Bake until a cake tester inserted into centers comes out clean, 15 to 20 minutes. Let cool completely in tin on a wire rack.
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