In a large bowl, whisk together flour, brown sugar, baking powder, cinnamon, nutmeg, allspice, and salt.
Cut in cold butter until mixture resembles coarse crumbs.
In a small bowl, whisk together milk, egg, and vanilla extract.
Add to flour mixture and stir until just combined.
Gently stir in the apple.
Drop ¼ cupfuls of batter several inches apart on a baking sheet. Side Note: If you want to make small fritters, use a heaping tablespoonful.
Bake for 10-12 minutes, or until bottoms are golden brown and center is set. Side Note: If you are making small fritters, start checking for doneness at 8 minutes.
Remove to a wire cooling rack and turn the oven to broil.
After turning the oven to broil, prepare the glaze by whisking together powdered sugar, milk, and vanilla extract until smooth.
Brush a thin layer of glaze over fritters. Place under the broiler.
Broil for 2-4 minutes, or until tops start to turn golden and the glaze bubbles.
Carefully remove the baking sheet to a wire cooling rack.
Brush remaining glaze over the warm fritters.
Allow the glaze to harden and serve. Enjoy!
Side Note: These baked apple fritters are best eaten the same day.