Step 1

Heat oil in a deep-fryer or large saucepan to 375 degrees F (190 degrees C).

Step 2

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.

Step 3

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.

Step 4

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.

Step 5

Transfer donuts to a wire rack to cool.