In a large, high sided pot, heat the oil to 375-degrees.
In a large bowl, whisk together the flour, baking soda, salt, baking powder, nutmeg, and cinnamon.
In a separate bowl cream together the shortening and brown sugar. Add in the eggs, vanilla, mashed potatoes, and milk. Blend until fully incorporated.
Add the flour mixture, 1/3'd at a time and on low speed into the creamed shortening mixture until all the flour is fully incorporated and the dough is soft and pliable.
Turn the dough out onto a lightly floured surface.*Note - if the dough seems too sticky, knead in a little extra flour. You're looking for a soft dough but not an extremely sticky dough.
Roll the dough out to an approximately, uniformly ½" thickness.
Use a 3" round cookie cutter or biscuit cutter that has been dipped in flour and cut out as many circles as you can. Set them aside on a lightly floured surface.*Note - You can re-roll the scraps and continue cutting circles from the remaining dough.
Use your thumb to poke holes into the center of the circles (more flour on your hands may be needed) and gently stretch the donuts into shape.
Use a large slotted spoon or spider strainer and carefully place about 4-5 donuts in the hot oil to fry about 3-4 minutes on each side or until deeply golden brown.*Note - if the oil is too hot, the donuts will brown quickly and still be raw in the middle. Try and keep your oil temperature as constant as possible to avoid this. Or, if it's not hot enough, the oil will saturate the dough making your donuts greasy.
Carefully removed the cooked donuts from the oil (using the strainer) and place them into a bowl with the cinnamon sugar. Toss to coat.
Serve warm or at room temperature.