1) In a large skillet or pot, heat oil over medium heat until it reaches 350 degrees F.
2) Stir together flours, baking powder, cinnamon, sugar, and salt in a medium bowl. In a separate bowl, whisk together egg, milk, and vanilla. Stir wet stuff into dry stuff and stir until it’s just combined. Stir in melted butter until the batter is mostly smooth.
3) Dust a clean surface heavily with flour and scoop donut dough out onto the surface. Cover with flour and press the dough out into a 1/4-inch thick layer. Use a small round cookie cutter to punch out holes. You should get about 3 dozen.
4) Fry donut hole rounds in batches in 350 degree oil for about 90 seconds per side. Flip them as they fry so they don’t get too cooked/heavy on one side.
5) When donut holes are golden brown (probably around 3 minutes), remove with a slotted spoon and let drain on a few paper towels. Finish frying all the donut holes.
6) Stir together glaze ingredients and dunk each hole in the glaze. Use a fork to shake off extra glaze and let donut holes cool/harden a bit. Serve while warm or at room temperature.