Preheat your oven to 400 degrees Fahrenheit (or 200 C) and grease two doughnut pans.*
Whisk the sugar and lemon zest together in a large mixing bowl. Whisk in the buttermilk, oil, eggs, and vanilla.
In a separate bowl, sift the flour, cornstarch, baking powder, and salt.** Add this all at once to the liquid and whisk until well combined. The batter will still seem quite liquidy.
Transfer the batter to a measuring cup, or anything with a spout, and slowly pour the batter into each doughnut cup, filling about 3/4 full. Bake for 8 to 10 minutes until the doughnuts spring back to the tough, but there is no browning on the top. Cool doughnuts for 10 minutes and prepare your topping of choice.
For the coating, whisk the sugar and lemon zest together. While the doughnuts are still warm, roll them in the sugar mixture and set aside to finish cooling.
For the glaze, whisk together the icing sugar, milk and vanilla until smooth. Take one doughnut at a time and dip the top of the doughnut into the glaze without dropping it and coat the doughnut generously. Allow excess glaze to drip off and set aside on a rack to set. If you want to add sprinkles, now is the time to do it!