In a large bowl, combine organic cookie mix and 10 tablespoons of butter. Use your hands to break up the butter into very small pieces. Add the cold water and mix until a dough forms. Divide dough in half, then form each half into flat discs and wrap with plastic. Chill 15 minutes or until firm enough to roll out.
Melt 1/4 cup of butter in a large non-stick skillet over medium heat. Add sliced apples and toss to completely coat with butter. Add brown sugar, cane sugar, cinnamon, vanilla, allspice and salt. Heat until the sugar has caramelized and the apples have softened, about 5 minutes.
Combine water and cornstarch in a small bowl. Pour cornstarch mixture into apples, then stir and cook until mixture is thickened, about 3 minutes. Remove from heat and cool completely.
Preheat oven to 350 degrees and line a cookie sheet with parchment paper. Remove dough from refrigerator and flour a flat surface. Roll out each dough to ¼” thick. Spoon cooled apple mixture evenly over one of the doughs; spread mixture all the way to the edges of dough.
Use a knife to trim the edges of the remaining dough, then cut dough into ¼” wide strips. Weave the dough strips over the apple mixture. Flour a round cookie cutter or drinking glass, then press cutter through dough making 8 cookies.
Transfer cookies to prepared pan. In a small bowl, whisk together the egg and remaining tablespoon of water. Brush egg mixture over the tops of each cookie, then sprinkle with sugar.
Bake 25-30 minutes, or until cookies become golden and apple mixture starts to bubble. Remove from oven and cool on cookie sheet 10 minutes before transferring to a wire rack. Enjoy immediately!