Step 1

Preheat the oven to 350 degrees F. Line the bottom of an 8x8 baking dish with parchment paper.

Step 2

Make the brown butter: In a small pan set over medium heat, melt the butter and cook until it turns brown and smells nutty, about 5 minutes. Try not to walk away from the butter, as it can go from brown to burned very quickly. Pour the brown butter into a large mixing bowl and let it cool slightly.

Step 3

Whisk together the flour, baking powder, and salt to combine.

Step 4

Add both sugars to the brown butter, and mix on medium speed with a hand mixer until well combined, about 2 minutes. Add the eggs and beat for another 2 minutes, until the mixture has lightened in color. Add the vanilla, and beat for 30 seconds.

Step 5

With the mixer on low, slowly add the flour mixture, and stop mixing right before the flour disappears.

Step 6

Add the chopped walnuts, then finish stirring by hand with a spatula, just until the flour is fully mixed in.

Step 7

Pour the mixture into the prepared pan and bake for about 35-40 minutes, until a toothpick inserted into the center comes out clean. Cool on a wire rack, and cut into squares. Enjoy!