Preheat oven to 350 degrees F.  Butter a 9 by 13 inch pan.

Make the cake.  In a large bowl, stir together the spices, flour, baking soda, and baking powder.

In another large bowl, cream the sugar and butter until light and fluffy.  I did this by hand but a hand or stand mixer will work too.  Beat in the maple syrup followed by the eggs and egg yolks, one at a time.  Beat in the vanilla.

Alternately add the flour mixture and applesauce, beginning and ending with the flour.  Stir in the apples and pecans and spread into the prepared pan.  Bake about 35 minutes and cool completely in the pan before glazing.

Once the cake is cool, make the glaze.  In a medium bowl, stir together sugar and cinnamon.  Stir in vanilla and maple syrup, then slowly add milk until a thick but spreadable consistency forms.  Drizzle over cake and allow to set for at least 15 minutes before serving.

Cake may be stored in an airtight container at room temperature for up to 5 days or frozen in pieces wrapped in parchment and foil and placed in a zipper bag for up to 3 months.  Thaw at room temperature about an hour or in the microwave about 1 minute.