Whisk all the dry ingredients, including the flour, yeast, sugar, salt, and apple pie spice, together.
In a separate bowl, mix together the softened unsalted butter, milk, eggs, and caramel extract.
Blend the liquid ingredients with the dry ingredients.
Let the dough rise for an hour or more, 'til doubled in size.
Roll the dough out onto a floured surface, and cut with donut/donut hole cutter. (TIP: If you don't have a donut hole cutter, cut the top off a plastic soda bottle and wash. Use the opening of the soda bottle to cut out donut holes, works like a charm!)
Place the donuts on a cookie sheet and let rise 'til doubled in size.
Meanwhile, mix up the icing, blending all the ingredients together.
Fry the donuts and donut holes in a deep fryer set to 350° F, 'til each donut hole is cooked thru and golden. You can also fry them in a skillet in a couple inches of canola oil.
Let the donuts and donut holes drain on paper bags.
While still warm, dip each one in the icing.
Set on a rack over wax paper to drip and cool.
Once they've cooled enough to eat, they're ready for you to enjoy!