In a large, high-sided skillet, heat the oil to 375-degrees F on an instant read thermometer.
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 dry ingredients (in three one third increments) on low speed into the wet ingredients until all the flour is fully incorporated, and it forms a dough that 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.
Use a rolling pin to roll the dough out into a uniform ½" thickness.
Use a 3" round cookie cutter or biscuit cutter that has been dipped in flour, and cut as many circles as you can from the first roll.Set the cut circles 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 each dough circle (more flour on your hands may be needed) and gently stretch the donuts into shape. Place the shaped donuts back on the lightly floured surface.
Use a large slotted spoon or spider strainer to carefully place 4-5 donuts into the hot oil to fry about 3-4 minutes on each side, or until the donuts are deeply golden brown.FYI - A wooden skewer is a great way to easily flip the donuts to fry both sides.*Note - if the oil is too hot, the donuts will brown quickly and still be raw in the center. Try and keep your oil temperature as constant as possible to avoid this. Or, if the oil is not hot enough, the oil will saturate the dough making your donuts heavy and greasy.
Carefully removed the cooked donuts from the oil (using the strainer) and place them directly into a bowl with the cinnamon sugar. Toss to coat the donuts evenly.Continue the same process with the remaining dough, and donuts.
Serve warm or at room temperature.
Notes
Store donuts in an airtight container at room temperature for up to 3 days.Store donuts in an airtight container in the refrigerator for 5-7 days.May be frozen. Store in an airtight freezer container or freezer bag. Label and date. Freeze for up to 2 months. Thaw in the refrigerator overnight.*Tip - to check if your oil is up to temperature without an instant-read thermometer, dip the handle of a wooden skewer in the hot oil, and if small bubbles immediately form on the skewer (think champagne bubbles), you're good to go.