Whisk first 8 ingredients in medium bowl to blend.

Using electric mixer, beat sugar and butter in large bowl until blended (mixture will be grainy). Beat in egg, then egg yolks, and vanilla. Gradually beat in buttermilk and then beat in pumpkin in 4 additions. Using rubber spatula, fold in dry ingredients in 4 additions, blending gently after each addition. Cover with plastic; chill 3 hours up to 24 hrs. 

Sprinkle 2 rimmed baking sheets lightly with flour. Press out 1/3 of dough on floured surface to 1/2- to 2/3-inch thickness. (Add more flour, by the tablespoon, if you can't pat it down and cut out rings due to stickiness). 

Using 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 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 if desired).

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 doughnuts, 3 or 4 at a time, until golden brown, adjusting heat to maintain temperature, about 1 minute per side. Using slotted spoon, transfer doughnuts to paper towels to drain. Cool completely. For doughnut holes, fry holes in 2 batches until golden brown, turning occasionally, about 2 minutes. Using slotted spoon, transfer to paper towels to drain and cool.

Combine butter, milk, corn syrup, and vanilla in medium saucepan and heat over medium heat until butter is melted and milk is slightly warmed. Decrease the heat to low, add the chocolate, and whisk until melted. Turn off heat, add icing sugar, and whisk until smooth. Dip the doughnuts immediately. Allow glaze to set for 30 minutes before serving.