In a large heavy-bottomed saucepan, pour enough oil to fill the pan about a third of the way. Heat over medium heat until a deep-frying thermometer inserted in the oil reaches 375 degrees F. Once the temperature reaches 365 degrees F, reduce the heat slightly to make sure it doesn't go above 385 degrees F.
In a mixing bowl, whisk together the milk, sour cream, vanilla and egg.
In a stand mixer fitted with a paddle attachment, combine the flour, sugar, baking powder, salt and nutmeg, about 1 minute, on low speed. With the mixer running, add the wet ingredients to the dry in a slow stream. The donut batter should be thicker than pancake batter.
Line a half sheet pan with paper towels.
Using two spoons, carefully drop spoonfuls of the batter into the hot oil and fry until golden brown, flipping halfway through cooking, 1 to 2 minutes.
Use a large metal slotted spoon to remove the donuts from the oil and place on the prepared half sheet pan to drain. Rest the donuts until cool enough to handle, but still warm. Toss the donuts with sugar and enjoy!