Prepare the dough, cut out, and fry:

Meanwhile, set a wire rack over a baking sheet. Combine in a large saucepan:

Cook the glaze over medium heat, whisking constantly, until the mixture just begins to simmer and is completely smooth. Remove the pan from the heat.

While the fried doughnuts are still warm, drop them into the glaze one at a time, turning to glaze both sides. Using a chopstick or long skewer, transfer the doughnuts to the wire rack. If the glaze stiffens while you are dipping the doughnuts, warm it briefly over low heat. Let the doughnuts stand about 15 minutes, or until the glaze is dry.