Mix shortening and sugar until fluffy.
Add eggs one at a time, beating completely after each addition.
Add apple juice concentrate and buttermilk and beat until combined.
In a separate bowl, whisk together flour, baking powder, baking soda, salt, and pumpkin pie spice.
Add flour mixture to the liquid mixture and beat until just blended. The dough will be very soft. it will be about the consistency of chocolate chip cookie dough.
Carefully lay a sheet of plastic wrap on top of a baking sheet.
Transfer dough to the plastic wrap.
Lightly flour a rolling pin and roll dough ot to about ½" thick.
Top with another layer of plastic wrap and transfer the pan to the freezer for about 20 minutes or the refrigerator for 1 hour.
While dough is chilling, you can prepare the spiced sugar topping.
When the dough has chilled, remove from freezer/refrigerator.
Using a round cookie cutter, cut circles out of the dough. Using a smaller cookie cutter (I used a heart) cut out the centers. Reserve them to fry up for bite-size goodness.
Place cut dough pieces on a lightly floured baking sheet. When all the dough has been cut out, place the pan back in the refrigerator while you prepare the oil for frying.
In a large, deep saucepan or Dutch oven, heat 1 quart of oil over medium heat to 325° (using a candy thermometer). While oil is heating, line a plate or baking sheet with paper towels.
When the oil is hot, carefully place a few pieces of dough into the hot oil (don't crowd the pan, but you can probably get away with cooking 3-4 at a time, at least).
The dough will sink down and then rise to the surface. Check the bottom side; if it's golden brown, flip the doughnut. If it's still a little pale, give it another 30 seconds or so and then check it again. After you've flipped the doughnut, the other side will cook significantly faster, so keep an eye on the. All in all, they should take about 90 seconds-2 minutes to cook completely.
Remove doughnuts from hot oil with a heat-proof slotted spoon and transfer to paper towels, followed by a baking rack (if you need the paper towel space for more doughnuts).
Repeat frying process with remaining dough and then with the holes-the doughnut holes will cook EXTREMELY quickly, so be careful not to burn them.
Place spiced sugar mix in a large Ziploc bag and then shake a few doughnuts at a time in the mixture.
Makes about 24-36 doughnuts (plus as many doughnut holes), depending on how big you cut the doughnuts and how many times you roll out the scraps.
