Whisk together the flour, sugar, baking powder, salt, and nutmeg in a large bowl.

In another bowl, beat the eggs, then add the melted butter, sour cream, and vanilla extract. Mix well.

Gradually add the wet ingredients to the dry ingredients, mixing until a sticky dough forms.

Cover and chill the dough in the fridge for at least 30 minutes.

Roll out the dough on a floured surface to about 1/2-inch thickness. Cut out donut shapes with a donut cutter or round glass, using a smaller cutter for the holes. Re-roll the scraps to use all the dough.

Heat vegetable oil in a deep fryer or heavy pot to 350°F-375°F. Fry 2-3 donuts at a time for about 1-2 minutes per side, until golden brown.

Transfer to a wire rack lined with paper towels and let cool slightly before glazing or coating with sugar.