For spiced sugar topping: Whisk all ingredients in a medium bowl to blend. Set aside.

For doughnuts: Whisk first 8 ingredients in a medium bowl to blend. Using an electric mixer, beat sugar and butter in a large bowl until blended (mixture will be grainy). Beat in egg, then yolks and vanilla. Gradually beat in 1/2 cup plus 1 tablespoon buttermilk; beat in pumpkin in 4 additions. Using a rubber spatula, fold in dry ingredients in 4 additions, blending gently after each addition. Cover with plastic; chill for 3 hours.

Sprinkle 2 rimmed baking sheets lightly with flour. Roll out 1/3 of dough on a floured surface to 1/2 to 2/3-inch thickness. Using a 2 1/2-inch diameter round cutter, cut out dough rounds. Arrange on sheets. Repeat with remaining dough in 2 more batches. Gather dough scraps. Press out dough scraps and cut out more dough rounds until all dough is used.

Using 1-inch diameter round cutter, cut out center of each dough round to make doughnuts and doughnut holes.

Line 2 baking sheets with several layers of paper towels. Pour oil into large deep skillet to depth of 1 1/2 inches. Attach deep fry thermometer and heat oil to 365°F to 370°F. Fry doughnut holes in 2 batches until golden brown, turning occasionally, about 2 minutes. Using a slotted spoon, transfer to paper towels to drain. Fry doughnuts, 3 or 4 at a time, until golden brown, adjusting heat to maintain temperature, about 1 minute per side. Using a slotted spoon, transfer doughnuts to paper towels to drain. Cool completely.

Add doughnuts and doughnut holes to bowl of spiced sugar and toss to coat. Serve immediately.