Prep the apples: Peel, core, and dice the apples into small 1/4-inch pieces. Toss with the lemon zest in a bowl and set aside.
Whisk the dry mix: In a large bowl combine the flour, baking powder, cinnamon, and salt.
Make the wet mix: In a separate bowl whisk together the milk, applesauce, vanilla, and brown sugar until the sugar is mostly dissolved.
Form the batter: Pour the wet mix into the dry ingredients and stir just until no dry flour remains. Fold in the apples. The batter will be thick and spoonable. Let it rest for 10 minutes to hydrate while you heat the oil.
Heat the oil: Pour oil into a deep, heavy pot to a depth of about 1 1/2 inches and set over medium heat. Bring to 360–365°F, adjusting the heat as needed to maintain the range.
Stir up the glaze: In a medium bowl whisk the powdered sugar, milk, apple cider, and vanilla until smooth and pourable but still opaque. Set a wire rack over a sheet pan for glazing and draining.
Fry the fritters: Using two spoons, drop heaping 1/4-cup mounds of batter into the hot oil, 3–4 at a time to avoid crowding. After 30 seconds, gently press each mound to flatten slightly. Fry 2 to 2 1/2 minutes per side until deep golden and cooked through (internal temp about 200°F).
Drain and glaze: Transfer fritters to the rack and let excess oil drip for 2 minutes. Dip the tops into the glaze or spoon glaze over both sides. Let set for 5 minutes; for a thicker finish, add a second light coat after the first sets.
Serve: Enjoy warm. Keep cooked fritters warm in a 250°F oven while you finish frying remaining batches.