Line a baking sheet with paper towels.
Add several inches of vegetable oil to a large heavy-bottomed stock pot set over medium heat. (There should be at least 3 inches of space between the top of the oil and the top of the stock pot.) Attach the deep-fry thermometer to the side of the pot and begin heating the oil while you make the batter.
In a medium bowl, whisk together the flour, sugar, baking powder, cinnamon and salt.
In a separate small bowl, whisk together the milk and egg. Add the wet ingredients to the dry then add the melted butter and stir together the batter just until combined. Fold in the diced apples.
Once the oil has reached 350ºF, use a small ice cream scoop (or two small spoons) to drop about 1-tablespoon scoops of dough into the oil, careful not to overcrowd the pan. Fry the fritters, flipping them in the oil until they're golden brown on all sides, about 2 minutes total. Using a slotted spoon, transfer the fritters to the paper towel-lined baking sheet. Repeat the scooping and frying process with the remaining batter, returning the oil to 350°F between each batch.
Allow the fried fritters to cool slightly before dusting them with confectioners' sugar and serving immediately.
The doughnut holes expand when fried, so 1-tablespoon scoops of dough will yield fritters that are roughly 2 inches in diameter.