Preheat your oven to 350°F (175°C). Line an 8×8-inch baking pan with parchment paper, leaving overhang on two sides. Lightly coat with nonstick spray.
Spread the walnuts on a baking sheet and toast for 8–10 minutes, stirring halfway through. Remove, cool slightly, and roughly chop.
Place the mashed bananas in a large mixing bowl.
In a light-colored saucepan over medium-low heat, melt the butter. Continue cooking until it foams, turns golden, and develops brown specks with a nutty aroma. Remove immediately from heat.
Pour the browned butter into the bowl with the bananas and whisk together.
Add honey and brown sugar. Whisk until smooth.
Allow the mixture to cool to lukewarm, then whisk in the egg and vanilla extract.
In a separate bowl, combine both flours, cinnamon, baking powder, baking soda, and salt.
Add the dry ingredients to the wet mixture. Fold gently until just combined. Do not overmix.
Fold in the toasted walnuts.
Transfer the batter to the prepared pan and smooth the top.
Bake the Banana Bread Brownies for 22–25 minutes or until a toothpick inserted into the center comes out clean.
Cool completely in the pan before frosting.
Brown Butter Frosting
Brown the butter using the same method as above.
Transfer to a mixing bowl and cool slightly.
Whisk in powdered sugar, vanilla, and enough cream to achieve a smooth, spreadable consistency.
Spread evenly over cooled brownies.
Slice into squares and serve.