Heat vegetable oil in a large skillet or pot over medium heat until it reaches 350 degrees F.

In a medium bowl, combine the all-purpose flour, whole wheat flour, baking powder, cinnamon, sugar, and salt. Stir well to ensure even distribution.

In a separate bowl, whisk together the egg, milk, and vanilla extract until well combined.

Gradually add the wet mixture to the dry ingredients, stirring gently until just combined. Stir in the melted butter until mostly smooth.

Dust a clean surface with flour, scoop the donut dough onto it, and press the dough out into a 1/4-inch thick layer.

Using a small round cookie cutter, punch out circles from the dough to yield about three dozen donut holes.

Drop the dough rounds into the preheated oil in batches. Fry for about 90 seconds per side, flipping them until golden brown.

Remove them with a slotted spoon and let them drain on paper towels.

In a bowl, mix together the powdered sugar, milk, and maple syrup until smooth.

Dunk each donut hole into the glaze, allowing excess to drip off. Let them cool slightly before serving.