In a large bowl, stir together the all-purpose flour, white sugar, baking powder, salt, and ground cinnamon until everything is well mixed. This forms the base for the batter, ensuring even distribution of the leavening and seasoning.
Add the plain applesauce and milk to the bowl of dry ingredients. Mix gently until just combined—you want the batter to be uniform, but be careful not to overmix, as that can make the fritters tough. I find using a spatula works best for this step.
Gently fold in the diced apples to the batter from Step 2. Make sure the apple pieces are evenly distributed throughout the mixture. The batter should now be thick and lumpy with apple pieces peeking through.
Heat about 2 inches of vegetable oil in a large skillet to 375°F (190°C). Carefully scoop about 1/3 cup of the batter (from Step 3) for each fritter into the hot oil, flattening slightly with your scoop or a spoon. Cook on one side for 2-3 minutes, or until golden brown, then flip with tongs and continue cooking for another 1-2 minutes until both sides are golden and cooked through. Remove the cooked fritters and place them on a cooling rack set over a pan or parchment paper to catch the excess oil. Repeat for remaining batter. I always use a thermometer to check the oil temperature for even frying.
In a medium-sized bowl, whisk together the powdered sugar, milk, and vanilla extract until the mixture is smooth and pourable. Adjust consistency with a tiny splash more milk if needed. For extra flavor, I like to add a tiny pinch of salt to balance the sweetness.
Dip each warm fritter (from Step 4) into the glaze (from Step 5), coating both sides. Place the glazed fritters back on the cooling rack and let the glaze harden while excess glaze drips down. Serve warm or at room temperature for the best texture.