Heat oven to 350°F. Grease a 9×13-inch baking dish.
Toss apples with lemon juice, 2 tablespoons brown sugar, and 1/2 teaspoon cinnamon. Set aside.
Whisk flour, granulated sugar, baking powder, salt, remaining cinnamon, and nutmeg in a large bowl.
In another bowl, whisk whole milk, beaten eggs, 2 teaspoons vanilla, and melted butter until smooth.
Stir wet mixture into dry ingredients just until combined. Do not overmix.
Fold in the apple mixture and any juices.
Spread batter in the pan. Sprinkle remaining brown sugar over the top and lightly swirl.
Bake 32–38 minutes, until golden and a tester comes out clean.
Whisk powdered sugar, glaze milk, and remaining 1/2 teaspoon vanilla until smooth.
Cool casserole 10 minutes. Drizzle with glaze. Serve warm.