In a large bowl, combine flour, cornstarch, baking powder, baking soda, salt, and nutmeg.
In another bowl, beat the sugar, melted butter, and eggs for about 3 minutes. Add vanilla extract and buttermilk, and continue beating for 2 more minutes.
Slowly add the dry ingredients a cup at a time until all the flour mixture has been added and it forms a sticky dough.
Wrap the dough in plastic wrap and chill for an hour in the fridge.
When ready to fry, line a cookie sheet with parchment paper and set it aside.
Remove the dough from the fridge and place it on a floured surface. Roll it out to about ½-inch thickness. Cut into doughnuts using a donut cutter if you have one available. If not, use two round cookie cutters, one small approx. 1-inch round cutter, and a larger 4-inch round cutter. Place on prepared cookie sheet. Use the larger one to cut out the doughnuts, then cut out the holes with the smaller one.
A 5-quart Dutch oven or cast iron pan works great for frying. Pour the oil for at least 3 inches or 5 centimeters deep.Note: Oil that's too low will cause the doughnuts to flatten, and too high can cause the hot oil to overflow. Heat oil until it reaches 375℉ (190℃). For safer results, check the oil's temperature with a thermometer. If you don't have a thermometer, a wooden chopstick or the handle of a wooden spoon dipped into the hot oil will make it bubble steadily if ready.
While the oil heats, line a plate or baking sheet with double paper towels to soak up excess oil before transferring them to a cooling rack.
Once the oil has reached 375℉ (190℃), turn the heat down to medium-low. You're set to start frying.
Working in batches, add the doughnuts to the oil and fry for 3-4 minutes, carefully flipping halfway through cooking. The doughnuts will be golden brown and cooked through.
Remove the doughnuts from the frying pot with a large slotted spoon or skimmer and lay them on the prepared plate. As soon as the first one is cool enough to touch, break it open to make sure it's cooked through.
Repeat in small batches until all the doughnuts are finished. Don't forget to fry up the doughnut holes, too.