Preheat oven to 350°F (175°C) and spray an 8×8 baking dish with cooking spray.
In a large bowl, combine the cookie mix (reserve the cinnamon mixture), egg, and butter. Mix until a dough forms.
Press about 2/3 of the dough into the prepared baking dish, reserving the other 1/3.
Spread the apple pie filling on top of the pressed dough.
Drop the remaining 1/3 of prepared dough on top of the apple pie filling.
Sprinkle the reserved cinnamon and sugar mixture on top.
Bake in the preheated oven for 50-55 minutes.
Allow to cool completely, then mix the glaze in a small bowl. Add a little milk at a time until you reach the desired consistency.
Drizzle glaze over the entire dessert and cut into desired sized squares.