In a large mixing bowl, whisk together the flour, sugar, baking powder, baking soda, salt, nutmeg, and cinnamon.

In another bowl, mix the buttermilk, eggs, melted butter, and vanilla extract until well combined.

Gradually add the wet mixture to the dry ingredients, stirring until just combined.

Cover the dough and refrigerate for about 30 minutes.

On a floured surface, roll out the dough to about 1/2 inch thick.

Use a donut cutter to cut out the donuts and holes.

In a deep fryer or heavy pot, heat the oil to 350°F.

Carefully place the donuts in the hot oil, frying for about 2-3 minutes per side until golden brown.

Use a slotted spoon to remove the donuts and transfer to a cooling rack.