Make the glaze by mixing all of the ingredients in a bowl until smooth and set aside. It might dry a bit while you do the rest of the prep work, but stirring will fix that; if it dries too much, add another splash of milk.
Preheat your oven to 400℉. Fritters use the broiler later, so move an oven rack close to the top. We'll be using a plain baking sheet -- no silpat or parchment paper -- because of the heat.
In a bowl, combine the flour, brown sugar, baking powder, cinnamon, nutmeg, and allspice. Cut in the butter until the mixture takes on a sandy consistency. A pastry blender is handy but not mandatory; I usually use a fork.
Whisk the milk, vanilla, and egg together in another bowl.
Add the milk mix to the flour mix and stir until it's about half combined. Add in the chopped apples and fold in to finish mixing.
Drop about a quarter cup of dough at a time on your baking sheet, leaving room between each dollop because it will spread a bit.
Bake for 11-12 minutes at 400 ℉. The fritters should be set and the bottoms starting to brown.
Remove the fritters from the oven and turn the oven to broil. Using a pastry brush, brush on the glaze over the hot fritters, and return them to the oven. Broil them for two minutes until the glaze is bubbly and the fritters start to brown.
Remove the fritters again, brush on a second layer of icing, and let rest. They can cool on the baking sheet for 10-15 minutes, before moving them to a wire rack to finish cooling.