In a medium bowl, mix together 2 1/2 cups flour, baking powder, salt, and baking soda. Stir in the cardamom and nutmeg and set aside.
In a large bowl, cream together the sugar and butter, then mix in the eggs and mashed potatoes.
Alternate adding the flour mixture and milk to the sugar mixture, starting and ending with the flour. The dough will be more like a very stiff batter when finished — add up to 1/2 cup flour, a little at a time, to achieve this consistency.
Pour vegetable oil into deep fryer or dutch oven and heat oil to 365°F.
Scoop dough onto a very well floured surface and knead to make stiff enough for rolling and cutting, adding more flour as required to prevent sticking.
Pat or roll dough 1/2-inch thick and cut out doughnuts and holes. (You can cook the holes or save to reroll the dough scraps.)
Place clean paper grocery bags on a cookie sheet, for draining doughnuts. (The bags will soak up excess oil.)
Fry doughnuts in batches for about 2 minutes per side, turning carefully with a wooden chopstick or fork. Drain doughnuts on prepared rack, and repeat with remaining dough, rerolling and cutting as needed.
Mix together the 1 cup sugar and cinnamon in a shallow bowl. When doughnuts have cooled for about 10 minutes, roll them in the cinnamon sugar and serve.
Doughnuts are best the day of, but extras can be stored in a paper bag.