Place the butter in a large saucepan and over medium-low heat. Once the butter melts, it will foam, turn clear golden, then begin to turn brown and smell nutty. Whisk often, scraping up any bits from the bottom. Watch the pan very carefully, as the butter will brown very soon after it begins to color and can burn quickly. Once the butter is deep golden and very fragrant, remove it from heat.
In a small bowl, whisk together the white whole wheat flour, all purpose flour, baking powder, and salt. Set aside.
Place rack in the center of your oven and preheat to 350 degrees F. Coat an 8x8 in pan with cooking spray, line with parchment paper so that the paper overhangs on the sides, grease once more and set aside.