Preheat your oven to 400°F and line a baking sheet with parchment paper to prevent sticking.
In a large bowl, whisk together the all-purpose flour, white whole wheat flour, brown sugar, baking powder, cinnamon, nutmeg, allspice, and salt.
Cut the cold butter into the flour mixture until it resembles coarse crumbs, ensuring the butter pieces are evenly distributed.
In another bowl, whisk together milk, egg, and vanilla extract. Pour this mixture into the dry ingredients and stir until just combined.
Gently fold in the chopped apple pieces, taking care not to overmix for the best texture.
Using a ¼-cup measuring cup, drop portions of batter onto the prepared baking sheet, spacing them evenly.
Bake in the preheated oven for 11-13 minutes, ensuring the bottoms are golden and the centers set.
Switch to broil mode for 2-4 minutes to achieve beautifully golden tops.
Whisk together confectioner's sugar, milk, and vanilla extract until smooth. Brush over warm fritters generously.
Serve the fritters warm for the best experience and enjoy the delightful balance of spice and sweetness!