Add the quart of oil to a large Dutch oven, reserving one tablespoon for the batter. Place the pot over medium-high heat. Monitor the temperature of the oil using a thermometer as it heats up. You'll be heating it to 350° to 375°F.
While the oil heats up, whisk the flour, sugar, cornstarch, baking powder, cinnamon, and salt together in a large mixing bowl.
Stir the milk, one tablespoon of oil, and vanilla extract together in a small container, then add the wet ingredient mixture to the bowl with the flour mixture. Stir just until the batter is combined.
Fold the apples into the batter.
Once the oil reaches 350°F to 375°F you can begin frying the fritters. Drop the batter in quarter cups into the hot oil, frying about three or four fritters at a time and ensuring that there's adequate space so that they aren't touching.
Fry the fritters for about three minutes on each side, or until they're golden brown. Transfer the fritters to a wire rack with a layer of paper towels underneath it when done, in order to allow the excess oil to drain.
Repeat the frying process until all of the batter is used.
Stir all ingredients for the icing together in a small bowl, adding extra powdered sugar if it seems too thin, or more milk if it seems too thick.
Drizzle the glaze over the fritters, or gently dip the tops in the glaze (if you like a lot of it).
Serve.