Melt the butter in a saucepan over medium heat. Continue cooking as it bubbles and then foams, sweeping a spatula across the bottom so the milk solids do not sit in one spot and burn. When golden-brown specks form on the bottom, remove from the heat and transfer to a bowl, scraping in the browned bits. Cool to room temperature. To speed cooling, place in the freezer for about 20 minutes, stirring every 5 minutes, just until room temperature.
Set the oven rack to the middle position and preheat to 325°F. Lightly grease two 9 × 4-inch loaf pans with gluten-free nonstick cooking spray. Line with parchment paper, leaving a 2-inch overhang. The long loaf pans shown in the photos, approximately 12 × 4½ inches, can also be used; their baking time is shorter.
Sift or whisk together both flours, kosher salt, baking soda, baking powder, cinnamon, nutmeg, cloves, ginger, and allspice in a medium bowl until evenly combined. Set aside.
Using an electric mixer on medium speed, cream the cooled browned butter and both sugars together until smooth. Add the eggs one at a time, beating thoroughly after each addition. Continue beating for 2 minutes until light and airy. Mix in the vanilla, then the pumpkin. Do not worry if the mixture looks slightly split or curdled after adding the pumpkin.
Add the dry ingredients and beat on low speed until just incorporated. Scrape down the sides of the bowl and gently fold by hand to finish mixing.
Divide the batter evenly between the prepared pans. Bake at 325°F for 60–70 minutes in two 9 × 4-inch pans, or 50–60 minutes in two long pans approximately 12 × 4½ inches. Test the center of each loaf with a toothpick or cake tester; it should come out clean. Cool in the pans for 10 minutes, then use the parchment to lift the loaves onto a wire rack. Cool completely.