In a medium bowl, whisk together the flour, baking powder, baking soda, salt, and nutmeg. Set aside.

In a large bowl, cream together the sugar and softened butter until light and fluffy. Add the egg, sour cream, and vanilla extract, mixing until well combined.

Gradually add the dry ingredients to the wet mixture, stirring until just combined. Do not overmix.

Cover the dough with plastic wrap and refrigerate for at least 1 hour, or until firm.

On a floured surface, roll out the chilled dough to about 1/2 inch thick. Use a doughnut cutter or two round cutters (one larger and one smaller) to cut out doughnuts.

Heat about 2 inches of vegetable oil in a deep pot or fryer to 375°F. Carefully drop the doughnuts into the hot oil, frying a few at a time until golden brown, about 2-3 minutes per side.

Using a slotted spoon, remove the doughnuts and place them on a paper towel-lined plate to drain excess oil.

Once cooled slightly, dust the doughnuts with powdered sugar before serving.