These are also delicious with cranberry or sour-cherry jam on the side.
Heat oil in a 5-quart saucepan over medium-high heat until it reaches 380 degrees on a deep-fry thermometer.
Meanwhile, heat sour cream in a heatproof bowl set over a saucepan of simmering water until just warm.
Whisk both flours, the granulated sugar, baking powder, baking soda, salt, nutmeg, and cinnamon together in a mixer bowl. Make a well in the center, and add yeast. Pour in sour cream, and let stand for 1 minute.
Whisk together buttermilk, egg and yolk, and vanilla, and pour into well in dry ingredients with the sour cream. Beat with a mixer on low speed until flour has been completely incorporated.
Sift a generous coat of flour onto a clean work surface. Turn dough out onto flour. Sift a generous coat of flour over dough. Pat dough to a scant 1/2 inch thick. (The dough will be very soft and sticky; use more flour if needed to keep it from sticking to the work surface.) Using a 1-inch cutter, cut out rounds, flouring cutter each time. Using a small offset spatula, place rounds on a lightly floured baking sheet, and let rest for 10 minutes. Gather scraps, and repeat.
Mix 1 1/4 cups granulated sugar thoroughly with 1 tablespoon cinnamon in a wide, shallow bowl.
Fry dough in batches of 6, turning each piece once, until golden brown, about 20 seconds per side. Using a slotted spoon, transfer doughnut holes to a baking sheet lined with paper towels, and let cool slightly. Roll warm doughnut holes in cinnamon-sugar mixture.