Adjust the oven rack to the lower third position and preheat your oven to 350°F (177°C). Positioning the rack lower helps prevent the top of the bread from browning too quickly. Lightly spray a 9×5-inch loaf pan with non-stick spray and set it aside.
You can mix everything by hand or with an electric mixer—both work well. I prefer using an electric mixer since it makes mashing the bananas easier. Using a handheld or stand mixer fitted with a paddle or whisk attachment, beat the mashed bananas, applesauce, and eggs together on medium-high speed until well combined. (You can also whisk by hand.) Add the honey, brown sugar, milk, and vanilla extract, then continue mixing on medium-high speed until fully blended. Set the mixture aside.
In a separate bowl, whisk together the flour, baking soda, cinnamon, and salt until well combined. Pour the dry ingredients into the wet mixture and mix on medium speed, or whisk by hand, just until everything is blended. Gently fold in the walnuts until evenly distributed.
Pour the batter into the prepared loaf pan and spread it evenly. Bake for 60–65 minutes, loosely covering the top with aluminum foil halfway through to prevent over-browning. The bread is ready when a toothpick inserted into the center comes out clean or with just a few moist crumbs. Since oven times can vary, start checking for doneness around the 55-minute mark and continue checking every 5 minutes until it’s perfectly baked.
Remove the bread from the oven and place the pan on a wire rack. Let it cool completely in the pan before slicing and serving to ensure clean cuts and the best texture.
Cover the banana bread tightly and store it at room temperature for up to 2 days, or in the refrigerator for up to 1 week. It actually tastes even better on the second day, once the flavors have had time to blend together.