In a Dutch oven, heat 1-inch of clean oil to 375 degrees F (190 degrees C).
While the oil is heating, sift together the flour, baking soda, and salt.
In a small bowl, whisk together the egg yolk, sugar, melted butter, and milk.
Add the wet ingredients to the dry and fold together until no streaks of flour remain, but try not to over mix.
Roll out the dough on a floured surface with a rolling pin to about 1/4-inch (1/2cm) thickness. Use a 3-inch (7 1/2cm) biscuit cutter to cut out six circles. Use a smaller cutter (a piping tip works) to cut out the middles.
Once the oil is hot, carefully slide three donuts into the oil. Fry for 15 to 20 seconds on the first side, then flip. Fry the other side for 15 seconds, or until golden brown, and then remove from the oil. Let rest on a paper towel lined cooling rack so the excess oil drips away. Repeat with the remaining donuts and donut holes.
Glaze
While cooling, whisk together the confectioner's sugar, milk, and vanilla extract in a shallow dish. Dip the donuts in the glaze, then serve.
If desired, add chocolate sprinkles to the glazed donuts while the glaze is still wet.