In place of the icing, try sprinkling these swirly doughnuts with a mixture of 2 tablespoons granulated sugar and 1/2 teaspoon pumpkin pie spice before baking.
For Doughnuts:
2 cups all-purpose flour
1/2 cup packed brown sugar
1 1/2 teaspoons baking powder
1 1/2 teaspoons pumpkin pie spice
1/2 teaspoon salt
1/4 teaspoon baking soda
1/2 cup canned pumpkin
2 eggs
1/4 cup milk
1/4 cup shortening, butter, or margarine, softened
For Icing:
1 cup sifted powdered sugar
1/4 teaspoon vanilla
3-4 teaspoons milk
FOR DOUGHNUTS: In a medium mixing bowl stir together flour, brown sugar, baking powder, pumpkin pie spice, salt, and baking soda. Add pumpkin, eggs, milk, and shortening, butter, or margarine; beat with an electric mixer on low speed till mixed.
Spoon the mixture into a pastry bag fitted with a large star tip with a 1/2-inch opening. Pipe onto 2 greased baking sheets in 3-inch circles. Bake in a preheated 375 degrees F oven for 10 minutes, or till golden brown. Cool doughnuts on a rack over waxed paper.
FOR ICING: In a small mixing bowl stir together powdered sugar and vanilla. Stir in enough milk to make a smooth icing of glazing consistency. Spoon icing over doughnuts.