On a lightly floured surface, roll out puff pastry.
Cut circles out of puff pastry using two different sized circle cookie cutters, a larger circle for the outside and a smaller circle for the center.
Fill a large pot with an inch of vegetable oil and heat over medium-high heat.
Cook donuts in hot vegetable oil, flipping when one side is golden.
In small mixing bowl, whisk together sugar, milk and vanilla for glaze.
While donuts are still hot, dip them in the glaze.