Preheat the Oven: Preheat the oven to 350℉ (180℃).
Grease Donut Pan: Generously grease a doughnut pan or a muffin tin (see instructions for a muffin tin in the notes).
Sift Dry Ingredients: Using a fine mesh sieve and sifting into a medium-sized bowl, sift together the flour, baking powder, pumpkin spice, and salt.
1 ¼ cups all-purpose flour, 2 teaspoons baking powder, 2 teaspoons pumpkin spice, ½ teaspoon salt
Mix Wet Ingredients: In a large mixing bowl, whisk together the pumpkin puree, brown sugar, milk and softened butter.
½ cup pumpkin puree, ½ cup light brown sugar, ⅓ cup whole milk, 4 Tablespoons unsalted butter
Combine Ingredients: Add the dry ingredients to the wet ingredients and mix until thoroughly combined.
Pipe the Batter: Transfer the batter to a piping bag and pipe it into a greased doughnut pan, or prepared muffin tin, filling each until it is ¾ full.
Bake: Transfer to the preheated oven and bake for 12-15 minutes, until a toothpick inserted in the middle of a doughnut comes out clean or the doughnuts bounce back when touched. Let the doughnuts cool in the pan for about 5 minutes, then remove them from the pan and place on a cooling rack.
Prepare Coating: While the doughnuts cool down, melt the butter for the coating in a small pot on medium heat. Be careful not to burn the butter.
4 Tablespoons unsalted butter
Coat the Doughnuts: Dip both sides of each doughnut into the melted butter and then into the cinnamon sugar to coat. It's okay to coat the doughnuts when they are still warm.
¼ cup cinnamon sugar
Serving: These doughnuts are best enjoyed on the day they are made!
Notes
Use a muffin tin as a doughnut pan: To use a muffin tin as a doughnut pan, roll small sheets of aluminum foil into cylinders. Make them tall enough so they are taller than the muffin pan. Then grease the muffin cups generously, together with the tin foil. Pipe the batter into the muffin tin and bake for 8 to 10 minutes until a toothpick inserted in the middle of a donut comes out clean. Doughnuts baked this way will bake for a shorter time as they are smaller than the bigger doughnuts baked in a doughnut pan.Make them vegan: To make these doughnuts vegan, substitute the butter for vegan butter or coconut oil and substitute the milk for plant-based milk such as oat or almond milk.Vanilla Glaze: Instead of coating the doughnuts in cinnamon sugar, you can make a vanilla glaze to drizzle on the doughnuts by combining confectioners' sugar with a splash of milk and a splash of vanilla extract.