In a small bowl mix the sugar and cinnamon and set aside.
In a medium bowl use a hand mixer to cream the sugar and butter until light and fluffy.
Add the eggs, sourdough starter, vanilla and milk and mix well.
Add the flour, baking powder and salt and beat just until the dry ingredients are incorporated. Do not overmix.
Allow the dough to sit 2 to 3 minutes to firm slightly. The dough should be soft but workable.
Lightly flour your counter and turn out the dough. Dust the top with flour and roll about 3/4" thick.
Use a round cutter to cut circles about 3 inches wide and a smaller cutter to cut out the centers.
Heat the oil over medium high heat in a heavy pot or skillet to a depth of about 3 inches. Just deep enough that the donuts don't stick to the bottom until the oil reaches 375 degrees.
Add the donuts in batches of 3 or 4, turning when golden brown on one side--about 2 minutes. Cook 1 to 2 minutes more then transfer to the cinnamon sugar and toss to coat.
Serve warm or at room temperature and may also be frozen for up to 2 months.