Step 1

Heat your oven to 350°F. Line an 8×8-inch baking pan with parchment paper, so that two opposite sides overhang like handles, then coat the paper with nonstick spray. Set aside. Spread the walnuts on an ungreased, rimmed baking sheet. Toast in the oven until fragrant and crisp, about 8 to 10 minutes, tossing once halfway through. Transfer to a cutting board and roughly chop.

Step 2

In a large mixing bowl, mash your banana (double check to make sure you have 1 cup).

Step 3

Brown the butter: Heat the butter in a small/medium light-colored saucepan over medium-low. This will take several minutes. Continue to heat until butter melts completely, foams and crackles, turns clear golden (the crackling will stop), then turns toasty brown, swirling the pan periodically. This entire process will take 3 to 5 minutes, depending upon your pan. Once the butter begins to smell lightly nutty, whisk it frequently, scraping up any browned bits from bottom. Watch the pan carefully in the last few minutes to ensure that the butter does not burn. As soon as the bits of butter in the bottom of the pan turn the color of a pecan, remove the butter from the heat and pour it immediately into the bowl with the banana to prevent the butter from burning, along with any toasted bits that are at the bottom. If you’ll be making the brown butter frosting, keep the pan handy.

Step 4

To the banana mixture, add the honey and brown sugar and whisk until smooth. At this point, the mixture should be cooled to lukewarm, but if it’s not, let it rest for a few minutes (or pop it into the fridge to cool it more quickly). Whisk in the egg and vanilla.

Step 5

In a small mixing bowl, stir together the all-purpose flour, white whole wheat flour, cinnamon, baking powder, baking soda, and salt. Add to the banana mixture. With a rubber spatula, gently and slowly fold just until the flour disappears. The batter will look lumpy. Fold in the walnuts.

Step 6

Scrape the batter into prepared pan and smooth the top with spatula. Bake for 22 to 25 minutes, until lightly browned at the edges and a toothpick inserted in the center comes out clean. Place the pan on a wire rack. Let cool in the pan completely if you will be frosting them. If not, wait at least 10 minutes before you lift the brownies from the pan using the parchment and cut them into squares. If they’re cool, the squares will be tidy; if they’re still warm, they’ll be messy. No one will mind.

Step 7

Brown the butter in the same sauce pan you used previously (unless it is super tiny, in which case, switch to a larger one), following the directions in step 3 above (if there are any burned bits of butter on the pan, wash them out first. If your pan is relatively clean, no need to wash in between). As soon as the butter is browned, remove the pan from the heat. Immediately, begin to stir in the powdered sugar with a rubber spatula or whisk, 1/4 cup at a time. If at any point it becomes too thick to whisk (likely by the fourth or fifth addition of powdered sugar), switch to a rubber spatula and add 1 tablespoon of the cream, then continue adding the powdered sugar, until the frosting is thick but spreadable. Stir in the vanilla extract. If needed, continue adding cream, 1 to 2 teaspoons at a time, until the frosting reaches your desired consistency (the butter might look like it's separating but just keep stirring. As long as you combine everything well, it will all cool together beautifully as the bars sit). Frost the cooled bars. Slice and enjoy!