Whisk first 8 ingredients in medium bowl to blend. Using electric mixer, ( or by hand ) beat sugar and butter in large bowl until blended (mixture will be grainy).

Beat in egg, and vanilla.
Gradually beat in buttermilk; beat in pumpkin or sweet potatoes in 2 additions.
Using rubber spatula, fold in dry ingredients in 2 additions, blending gently after each addition.

Cover with plastic; Chill 3 hours.
The dough will look very soft, must be cold to work with it. Dust your hands with flour to start working with the dough after it has been chilled.

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.
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 donuts and donut 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. If you do not have a thermometer test the oil with a bit of dough and see if the temperature is right.
If the dough is too dark with in seconds reduce the temperature. Donuts should be golden brown. on both sides.

Fry donut holes in 2 batches until golden brown, turning occasionally, about 2 minutes.

Using slotted spoon, transfer to paper towels to drain. Fry donuts, 3 or 4 at a time, until golden brown, adjusting heat to maintain temperature, about 1 minute per side. Using slotted spoon, transfer donuts to paper towels to drain. Cool completely.

Fry doughnut holes in 2 batches until golden brown, turning occasionally, about 2 minutes.

Using slotted spoon, transfer to paper towels to drain. Fry donuts, 3 or 4 at a time, until golden brown, adjusting heat to maintain temperature, about 1 minute per side. Using slotted spoon, transfer donuts to paper towels to drain. Cool completely.

Spiced sugar
1 cup sugar
4 teaspoons ground cinnamon
2 teaspoons ground nutmeg ( optional )
Whisk all ingredients in medium bowl to blend.
OR
Dust with powder sugar.

Chef's Note & Story

Donut dough MUST be Chill to work with it.

Had problems with the photos. Will add later.