1. Adjust an oven rack to the middle position and heat the oven to 350 degrees. Spray the bottom and sides of a 9 by 5-inch loaf pan with the nonstick baking spray. Mix the all-purpose flour, cake flour, baking powder, baking soda, salt, and 1/4 cup of the sugar together in a medium bowl; set aside. In a separate bowl, mix the mashed bananas, yogurt, and vanilla together; set aside.
2. Beat the remaining 1/2 cup sugar and butter together with an electric mixer on medium-high speed until light and fluffy, 3 to 5 minutes, scraping down the sides of the bowl with a rubber spatula as needed. Add the eggs, one at a time, beating well after each addition.
3. Reduce the mixer seed to low. Beat in half of the flour mixture until just incorporated, followed by one-third of the banana mixture, scraping down the bowl as needed. Add half of the remaining flour, followed by another one-third of the banana mixture. Repeat this process once more, being careful not to overmix the batter, which should look thick and chunky.
4. Scrape the batter into the prepared loaf pan and sprinkle the top evenly with the walnuts (if using). Bake until the loaf is golden brown and a toothpick inserted into the center comes out with just a few crumbs attached, about 55 minutes, rotating the pan halfway through the baking. Cool the bread in the pan for 10 minutes, then transfer the loaf to a wire rack. Server warm or at room temperature. (The bread can be wrapped with plastic wrap and stored at room temperature for up to 3 days).