Preheat the oven to 350 degrees F (175 degrees C). Lightly grease and flour a 10×5-inch loaf pan.
Sift all-purpose flour, whole wheat flour, baking powder, baking soda, salt, and cinnamon together.
Beat brown sugar, white sugar, and eggs in a stand mixer or with a hand-held electric mixer until light and fluffy, about 5 minutes. Reduce speed to low and slowly drizzle in olive oil until evenly combined. Beat in bananas, Greek yogurt, and vanilla extract until combined. Fold in 1/3 of the flour mixture with a spatula; repeat twice more until flour is fully incorporated.
Pour batter into the prepared loaf pan. Sprinkle walnuts and Demerara sugar over the top.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, 55 to 60 minutes.
Substitute sour cream for the Greek yogurt if desired.
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