In a large bowl, combine the warm milk and yeast then let it sit for 5 minutes until frothy.
Add the sourdough discard, sugar, melted butter, and egg. Mix until well combined.
Gradually add the flour and salt, mixing until a dough forms.
Then Knead your dough on a floured surface for about 10 minutes until it’s smooth and elastic. Alternatively, use a stand mixer with a dough hook attachment.
In a greased bowl place the dough, cover it with a damp cloth, and let it rise in a warm place for 1 to 2 hours until it has doubled in size.
When the dough has risen, punch it down to release the air.
Roll out the dough on a floured surface to about ½ inch thick.
Use a donut cutter or two round cutters of different sizes to cut out the donuts and the donut holes.
Heat oil in a deep fryer or a large pot to 350°F (175°C).
In hot oil, carefully drop a few donuts at a time the fry for 1 to 2 minutes on each side until golden brown.
Then remove the donuts with a slotted spoon and drain on paper towels.
Preheat your oven to 375°F (190°C).
On a baking sheet lined with parchment paper, place the shaped donuts.
Bake for about 10-12 minutes or until golden brown.
Mix the powdered sugar, milk, and vanilla extract in a small bowl until smooth.
Dip the warm donuts into the glaze, allowing the excess to drip off.
On a wire rack, place the glazed donuts to set.
