Preheat the oven to 350°F and line a cupcake tin with 12 paper liners.
In a large mixing bowl, whisk together the flour, brown sugar, baking powder, baking soda, salt, cinnamon, and nutmeg.
In a separate smaller bowl, whisk together the oil, applesauce, eggs, vanilla, and sour cream.
Pour the wet ingredients into the bowl of dry ingredients and whisk to combine.
Divide the batter between the 12 liners, filling each about halfway.
Bake for 12-15 minutes.
While the cupcakes bake, melt the butter in a saucepan over medium heat. Add apples, brown sugar, cinnamon, and lemon juice. Cook until apples become tender and release their juices.
Mix together the cornstarch and water and pour into the apple mixture. Continue to stir and heat until thickened and syrupy, about 2 minutes. Remove from heat and cool.
Preheat the oven to 400°F and line a baking sheet with parchment paper. Roll out pie dough and use pie crust punches to cut shapes, or cut small squares or circles.
Transfer shapes to the baking sheet and lightly brush with heavy cream. Sprinkle each piece with cinnamon sugar and bake for 8-10 minutes or until golden brown.
Using a hand or stand mixer with the paddle attachment, beat the butter and vanilla bean paste until smooth.
Sift in all of the powdered sugar and then pour in the milk. Mix on low speed to incorporate the sugar. Increase to medium speed and beat until smooth and creamy, about 2 minutes.
Pour in the heavy cream and mix on high speed for about 1 minute, or until light and fluffy.
Make sure the cupcakes have completely cooled before assembling. Fit a piping bag with a large round tip and fill with frosting.
Holding the tip in the very center of each cupcake, pipe a mound of frosting. Using a spoon or small offset spatula, dip into the center of the frosting to create a well.
Fill the center with about 1/2 tablespoon of cooled apple pie filling. Press in a cooled pie crust garnish and enjoy.