Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper.
In a medium bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, and nutmeg. Set aside.
In a large bowl, cream together the softened butter and brown sugar until light and fluffy. Add the egg and vanilla extract, and mix well.
Gradually add the dry ingredients to the butter mixture, alternating with the buttermilk. Mix until just combined. Fold in the chopped apples.
Drop rounded tablespoons of batter onto the prepared baking sheet, spacing them about 2 inches apart. Flatten each mound of batter slightly with the back of a spoon.
Bake for 10-12 minutes, or until the edges are lightly golden. Remove from the oven and let the cookies cool on the baking sheet for a few minutes, then transfer them to a wire rack to cool completely.
While the cookies are cooling, prepare the filling. In a medium bowl, beat the softened butter until creamy. Gradually add the powdered sugar, beating well after each addition. Add the applesauce and vanilla extract, and continue beating until the filling is smooth and fluffy.
Once the cookies have completely cooled, spread a generous amount of filling on the flat side of one cookie, then sandwich it with another cookie.
Repeat with the remaining cookies and filling until all the whoopie pies are assembled.
Serve the apple whoopie pies immediately, or store them in an airtight container in the refrigerator until ready to serve. They can be enjoyed chilled or at room temperature.