To Make the Brown Butter Pumpkin Spice Crumb Topping:
Begin by browning the butter. Place the butter in a light-colored skillet. (A light-colored skillet will help you determine when the butter begins browning.) Melt the butter over medium heat, stirring constantly. Once it’s melted, the butter will start to foam. Keep stirring. After 5 to 8 minutes, the butter will begin browning; you’ll notice lightly browned specks begin to form at the bottom of the pan, and you’ll start to smell a nutty aroma. Once the butter is browned, immediately remove it from the heat, and pour it into a medium heat-safe bowl.
Add the dark brown sugar, granulated sugar, pumpkin pie spice, and salt to the brown butter. Stir until the ingredients are evenly combined. Add in the flour, and mix with a fork until the flour is completely incorporated. Transfer the bowl to the fridge until you are ready to use the topping.
To Make the Pumpkin Muffins:
Preheat the oven to 425°F (220°C). Spray a 6-cup muffin pan with nonstick spray or line it with cupcake liners, then set it aside.
In a medium bowl, whisk together the flour, baking powder, baking soda, salt, and pumpkin pie spice until the ingredients are combined, then set aside.
In a separate medium bowl, whisk the granulated sugar, brown sugar, oil, and pumpkin puree together until they are combined. Pour the dry ingredients into the wet ingredients, then fold everything together gently until just combined and no flour pockets remain.
Spoon the batter into the prepared muffin pan, filling each cup almost full; you’ll use 4 to 4½ tablespoons (90 g) of batter per cup. Take the crumb topping out of the fridge. Evenly sprinkle the mixture on top of the muffin batter. After adding the crumb topping, gently press the crumbs down into the batter so they stick when the muffins rise in the oven.
Bake the muffins for 5 minutes. Keeping the muffins in the oven, reduce the oven temperature to 350°F (180°C), and bake them for 15 to 17 minutes, or until a toothpick inserted into the center comes out clean. Allow the muffins to cool for 10 minutes in the pan before removing them to a wire rack to cool completely.
Cover leftover muffins tightly, and store them at room temperature for 1 to 2 days or in the refrigerator for up to 1 week.
If you don’t have pumpkin pie spice, you can use 1/8 teaspoon each of cinnamon, nutmeg, ginger, and cloves for the crumb topping and 1 teaspoon cinnamon, ¼ teaspoon nutmeg, and 1/8 teaspoon each of ginger and cloves for the muffins.