Mix the warm milk and yeast in a bowl and allow to proof for 5 minutes.
In another bowl, mix the egg and sugar until creamy and pale. Add the warm milk and yeast, as well as buttermilk and melted butter.
Stir in the flour and salt and knead at least 10 minutes to obtain an elastic, smooth dough. If you have a stand mixer, this part is fairly easy.
Cover the bowl with plastic wrap and allow to proof for 1 hour at room temperature or overnight in the fridge.
Roll the dough into a thick sheet, about 8mm thickness then cut rounded shapes with a round cookie cutter. Using a smaller cutter, cut out the center of each donut.
Cover the donuts with a clean kitchen towel and allow them to proof for 30 more minutes.
Bring a few cups of frying oil to high temperature over medium to high flame.
Carefully drop each donuts in the hot oil and fry on each side just until golden.
Remove the donuts on paper towels.
Glaze:
Mix the sugar and milk in a bowl until creamy. The glaze should be fairly thick, but still run off the spoon. If it's too thick, add a few more drops of milk; if it's too thin, add more powdered sugar. If using food coloring, add just a tiny drop of you favorite color and mix well.
Dip each donut in the glaze and allow it to drip off the excess. Decorate with your desired sprinkles.
Notes
Replace the milk in the glaze with lemon juice, orange juice or fruit purees for differently flavored glaze.