1-1/2 qts. pure vegetable oil Coatings:
1 cup sifted confectioners' sugar
1 cup granulated sugar
2 Tbs. ground cinnamon
1 cup all-purpose flour
2/3-cup cake flour
1/2-tsp. baking soda
1 tsp. baking powder
1/2-tsp. ground nutmeg
1 large egg
1 Tbs. unsalted butter, melted
1/2-tsp. pure vanilla extract
1/2-cup buttermilk, room temperature
Attach a candy thermometer to the side of a 4-5 quart saucepan placed over medium heat. Pour in the oil (it should be 3-4 inches deep) and heat to 375-380 degrees F.
Prepare one or both coatings: Place the confectioners' sugar in a plastic bag. Place the granulated sugar and the cinnamon in another plastic bag, and shake (with the bag tightly closed) to mix thoroughly. Set the bags aside.
Sift both flours, baking soda, baking powder, salt and nutmeg together into a small bowl and set aside.
Using a whisk, blend the egg and sugar together in a medium-size bowl. Stir in the melted butter, vanilla and buttermilk.
Resift the flour mixture over the egg mixture, and using a rubber spatula, fold gently until mixed.
Using a 1-1/2 inch diameter ice cream scoop, drop five level scoops of the batter, one at a time, into the oil and cook until they are crunchy and deep golden (4-5 minutes).
Using a slotted spoon, remove a doughnut hole from the oil and cut it in half. If the center seems gooey, the doughnut holes need to cook for another minute or two. Remove the doughnuts with the slotted spoon and place them on paper towels to drain. Continue frying the remaining batter in this fashion.
To coat the doughnut holes in the cinnamon-sugar mixture, wait about 1 minute after removing them from the oil, then place one doughnut at a time in the bag and toss to coat. Return it to the paper towel to cool.
To coat with the confectioners' sugar, allow the doughnut holes to cool completely, then place them one by one in the bag and toss to coat.
These doughnuts should be eaten as soon as possible.