• Preheat oven to 350℉. Spray a 6-cavity doughnut pan with baking spray.
  baking spray
• To brown butter, add the cubed butter to a light-colored sauté pan over medium heat. Heat, whisking constantly.
  11 tablespoon unsalted butter
• Remove from heat once it is golden brown and has a nutty aroma.
• Pour your browned butter into a heatproof container, scraping the pan to get all the brown bits. Stir, and remove one tablespoon to reserve for glaze. Set both containers aside to cool slightly.
• In a medium bowl, whisk together flour, pumpkin pie spice, baking soda, baking powder, and salt until well mixed. Set aside.
  2 cups all-purpose flour, 1 tablespoon pumpkin pie spice, 1½ teaspoon baking powder, 1 teaspoon baking soda, ½ teaspoon salt
• Combine larger portion of brown butter with brown sugar in a large bowl and whisk until smooth.
  1 cups light brown sugar
• Whisk in eggs, vanilla, and pumpkin, mixing after each addition until smooth.
  2 large eggs, 2 teaspoon pure vanilla extract, 1 15-oz. can pumpkin purée
• Gradually fold in dry ingredients, mixing just until combined.
• Pipe or spoon batter into donut pan, filling just about to the top of each well. Bake in preheated oven 12-14 minutes, or until a toothpick entered into a donut comes out clean. Let cool completely on a wire rack.

Maple Brown Butter Glaze

• In a medium bowl, combine powdered sugar, the tablespoon of brown butter reserved from earlier, maple syrup, milk, and salt. Whisk together until smooth.
  1 cup powdered sugar, 1 tablespoon browned butter, 1½ tablespoon maple syrup, 1½ tablespoon milk, pinch salt
• Dip donuts face down into the mixture and let excess glaze drip off. Place donuts onto a wire rack to let the filling set before serving.