Preheat the oven to 350. Line 15 muffin cups with paper liners. In a medium bowl, whisk together the flours, baking powder, salt, allspice, and cinnamon.
In a large bowl, beat the butter and sugar together until light and fluffy. Add the eggs one at a time, mixing well after each addition. Add the vanilla and mix to combine. Add the flour mixture in three additions, alternating with the milk. Mix until just combined.
Scoop the batter into the prepared muffin cups, filling 3/4 full. Bake 16-18 minutes, until a toothpick inserted in the center comes out clean. Remove from the oven, move to a cooling rack, and let cool completely. Do not turn off the oven.
To make the pie crisps, roll out the pie crust and cut out circles from the dough. Place the circles on a parchment lined baking sheet and sprinkle with the turbinado sugar. Bake 8-12 minutes, until golden brown. Remove from the oven and let cool completely.
While the pie crisps are baking, combine all of the filling ingredients in a medium saucepan. Cook over medium heat, stirring frequently, until the apples are soft, about 6-8 minutes. Remove from heat and cool completely.
To make the frosting, beat together the butter, vanilla, ice cream, and salt until smooth. With the mixing speed on low, gradually add the powdered sugar. Once all of the powdered sugar has been added, turn the speed to high and beat 4-5 minutes, until fluffy.
To assemble the cupcakes, cut a small circle out of the center of each cupcake with a cupcake corer or paring knife. Scoop some of the apple filling into the center of each cupcake. Using an ice cream scoop, place a scoop of frosting on top. Add a pie crisp to the top of the frosting for garnish.