In a large bowl, sift together the flour, baking powder, baking soda, salt, nutmeg and 1/2 teaspoon cinnamon. Using an electric mixer fitted with a paddle, mix together the butter, granulated sugar and the brown sugar, until creamy. Mix in eggs one at a time. Mix in vanilla and buttermilk. Scrape down bowl and add sifted flour mixture. Mix just until blended. If the dough is too soft to roll, add in a few tablespoonfuls of flour to stiffen somewhat.
On a lightly floured work surface, roll out dough to a rough disk about 1/2-inch to 3/4-inch thick. Cut dough using a 2 1/2-inch doughnut cutter. Reserve "holes."
Set a wok on a secure wok stand or, alternately use a heavy guage stock pot and fill with oil. Heat to 365 . Putting three or four doughnuts in at a time, fry until deep golden brown on each side, about 2-3 minutes total. Drain on a platter lined with paper towels and cool for about 4 minutes. Fry "holes" separately.