In a large medium bowl combine flour, cornstarch, baking powder, baking soda, salt, and nutmeg.
In another bowl beat together 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 used up and it forms a sticky dough.
Wrap the dough in plastic wrap and chill for 1 hour in the fridge.
When ready to fry line a cookie sheet with parchment paper and set it aside.
Remove dough from the fridge and place on a floured surface. Roll out to about 1/2 inch thickness. Cut into doughnuts using a donut cutter, if you have one available. If not, use two round cookie cutter, about one 1-inch small round cutter, and a 4-inch cutter large round cutter. Place on prepared cookie sheet.
For frying, you can use a 5-quart dutch oven or cast iron. Pour oil into desired frying pot until it is at least 3 inches deep or about 5 centimeters high. Note: too low would cause the dough to flatten out.
Heat oil until it reaches 375 degrees F (190 degrees C). For best results or if you can use a thermometer to ensure oil is at the desired temperature.
While it heats up, line a plate or baking sheet with double paper towels to soak out excess oil before transferring to a cooling rack.
Once the oil has reached 375 degrees F, turn the heat down to medium-low. You are all set to start frying.
Working in batches, add the doughnuts to the oil and fry for 3 to 4 minutes, flipping halfway through cooking, or until the doughnut is golden brown and cooked through.
Use a large slotted spoon or skimmer to remove the donuts out of the fry pot to the prepared paper plate. Once I remove it from the heat I always do a taste test to make sure it is cooked through.
Repeat in small batches, until all the donuts are finished.