In a small pot warm the milk so that it is warm but not hot.
In a large bowl place the flour, sugar, salt, egg, milk and sourdough starter.
Mix thoroughly with a wooden spoon until it is well combined. It should form a soft but knead able dough.
Tip out on to a floured board and knead for 3-5 minutes.
Split the dough in to 24 even pieces. This is easily done by cutting it in half, then each half in half again. Then each of those halves split in to 6 pieces.
Roll the pieces in to balls and place them on a lined cookie sheet with about 1/2 an inch between them.
Place these somewhere warm to rise. If you do not have anywhere suitable in your house you can set your oven on very low until it is about 100F. Place a dish with 1/2 inch of boiling water in the bottom of the oven to create steam, turn your oven off, place the donut holes on the tray in the oven and close the door. Bread rises really well in a warm and steamy environment.
Leave the donuts to rise for about one hour. You can leave them for up to 6 hours to rise if you have other things to be doing. They will rise a lot further when they cook, so they don’t have to have risen too much before cooking.
While they are rising place the second measure of sugar and the cinnamon in a bowl ready for dusting the donut holes with.
Heat some oil in either a deep fryer or on the stove top to about 330F. Keep a close eye on the oil as it is flammable and keep children out of the kitchen while you are using it.
Place the donuts in the oil a few at a time. They will sink at first, but will rise to the top as they are cooking. Flip them over with some tongs or a slotted spoon when the bottom goes a rich golden color. It takes about 3 minutes on each side.
Once they are cooked drain them for 30 seconds and then pop them in the bowl of cinnamon sugar and roll them around.
Notes
They will keep in a sealed container for up to a week, but they are best eaten within 2-3 days. You can reheat them in a warm oven for 10 minutes.