In a stand mixer bowl, combine flour, sugar, baking powder, salt, cinnamon, and nutmeg
Add milk, eggs, and vanilla
Stir until just combined
Peel, core, and finely dice the apples into ¼–½ inch pieces
Toss the apple pieces with lemon juice
Add apples to the batter and fold to combine then set aside
Heat oil in a large pot to 375°F (190°C) over medium heat
Use a candy thermometer or test with a small drop of batter
Scoop heaping spoonfuls of batter using an ice cream scoop or two spoons
Gently lower batter to the surface of the oil before dropping in
Cook for 2–3 minutes then flip with a slotted spoon
Continue cooking until deep golden brown
Transfer fritters to a paper towel-lined sheet pan to cool
Repeat with remaining batter
In a small bowl, whisk together powdered sugar, milk, and vanilla
Drizzle glaze over cooled fritters
Serve immediately