Place rack in the center of your oven and preheat to 350 degrees F. Coat an 8x8 inch pan with cooking spray, line with parchment paper so that the paper overhangs on the sides, grease once more, and set aside.
In a small bowl, stir together the white whole wheat flour, all purpose flour, baking powder, and salt. Set aside.
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.
Whisk the brown sugar, maple syrup, and bourbon into the saucepan with the browned butter until smooth. Let cool to lukewarm, then whisk in the eggs, one at a time, and the vanilla.
Pour the maple butter mixture into the bowl with the dry ingredients and whisk by hand until combined. Fold in the chopped toasted walnuts.
Pour the mixture into the prepared pan. Bake for 20 to 25 minutes, until a toothpick comes out clean and the bars pull away from the sides of the pan slightly. For clean cutting, let cool completely. Use the parchment paper overhang as “handles” to transfer to a cutting board.
To prepare the glaze, whisk all ingredients together until smooth. Drizzle over bars, then slice bars into desired sizes and serve.
TO STORE: Keep leftover bars well-wrapped in the refrigerator or at room temperature for up to three days.
TO FREEZE: Maple bourbon bars may also be wrapped individually in plastic and kept in the freezer for up to three months. Defrost overnight in the refrigerator overnight before serving.