Heat oil in a deep-fryer or large saucepan to 375 degrees F (190 degrees C).
Beat sugar and shortening together in a bowl using an electric mixer until creamy. Add milk, eggs, and vanilla extract; stir well. Stir in mashed potatoes. Add flour, baking powder, salt, nutmeg, and cinnamon. Stir using a sturdy spoon, as mixture will be thick. Refrigerate dough for 1 hour so that dough will be less sticky and easier to work with.
Lightly flour a countertop and place plastic wrap on top of dough; roll out to desired thickness. Cut into strips or use a donut cutter to make traditional round donuts.
Lower donuts carefully into the hot oil in batches. Fry until 1 side is golden brown, 2 to 3 minutes. Turn and continue frying until other side is golden, about 2 minutes more. Transfer to a plate lined with paper towels to drain. Repeat with remaining donuts.
Transfer donuts to a wire rack to cool.
For lack of a donut cutter, I use a lid off of a Mason(R) jar and use a baby bottle to “cut” out the middle.
We have determined the nutritional value of oil for frying based on a retention value of 10% after cooking. Amount will vary depending on cooking time and temperature, ingredient density, and specific type of oil used.
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