Combine all-purpose flour, whole wheat flour, baking powder, baking soda, salt, cinnamon, nutmeg, and mace on wax paper.

Whisk the dry ingredients together until well blended.

In a separate bowl, cream together the vegetable shortening, sugar, eggs, and vanilla extract until thoroughly combined.

Stir in the applesauce and buttermilk until the wet ingredients are well mixed.

Gradually add the blended dry ingredients to the wet ingredients, mixing one cup at a time until smooth after each addition.

Refrigerate the doughnut dough for 2 hours.

Preheat oil in a deep fryer or large pot to 375°F (190°C).

Turn the refrigerated dough out onto a well-floured surface, using additional flour as needed for handling.

Roll out the dough to about 1/2 inch thickness.

Use a floured 2 1/2-inch doughnut cutter to cut out the doughnuts.

Remove the centers using a smaller cutter or knife.

Carefully lower a few doughnuts at a time into the hot oil.

Fry for about 1 minute on each side, or until golden brown.

Remove the fried doughnuts and place them on paper towels to drain excess oil.

While still warm, sprinkle the doughnuts generously with sugar.