In the bowl of a stand mixer fitted with a dough hook, add the flour, salt, baking powder, and sugar; stir to combine.

In a liquid measuring cup, whisk the eggs, orange juice, orange zest, vinegar, and orange extract until well combined. Add the shortening and gradually pour in the milk mixture and knead at medium speed until smooth and the mixture forms a ball, leaves the sides of the bowl, and climbs up the dough hook, about 5 to 10 minutes.Remove the dough from the bowl. Using your hands, form the dough into a smooth ball. Lightly oil a bowl. Place the dough in the bowl and turn it to oil on all sides. Cover with plastic wrap and let it rest for 15 to 30 minutes.

On a lightly floured work surface, roll the orange doughnuts into a log and cut about ½-inch thick pieces of dough, and roll each piece gently with your hands into a rope roughly ¼ inch thick. Shape the rope into a circle, bringing the ends together; keep in mind that they expand during the frying.

Alternately, you can divide it into golf-sized portions. Roll each piece into a ball, then use your finger to make a hole in the center of each. Next, gently stretch the balls to an oval ring. Continue the same process with the remaining dough. Place a sheet of plastic wrap over the rolled-out dough. The dough must stay moist. Set up a paper towel-lined sheet tray to place the crispy orange doughnuts when they come out of the oil.

Using a slotted spoon or spider, transfer the crispy orange doughnuts to the prepared baking sheet.While Crispy orange doughnuts are still warm, toss them in the cinnamon-sugar mixture to coat.crispy orange doughnuts are best served warm.