Peel, core, and finely chop the apples into small pieces, measuring about 2 cups. In a large bowl, whisk together the flour, sugar, baking powder, salt, and cinnamon.

In a separate bowl, whisk the eggs, whole milk, and vanilla extract. Add the wet mixture to the dry ingredients and stir just until combined.

Fold in the chopped apples. The finished batter should be thick and scoopable rather than pourable, with the apple pieces evenly distributed.

Heat 1 1/2 to 2 inches of vegetable or canola oil in a heavy-bottomed pot or deep skillet to 350°F (175°C). Drop the batter by heaping tablespoons into the oil in small batches.

Fry each fritter for about 2 to 3 minutes per side, turning once, until deeply golden brown and cooked through. Transfer the fritters to a wire rack or paper towels and allow the oil to return to about 350°F before cooking another batch.

Whisk the powdered sugar, milk, and vanilla until smooth, adding milk a few drops at a time if needed. Drizzle or spoon the glaze over warm fritters and let it set for several minutes before serving.