Warm the milk and mix with sourdough discard and sugar in a bowl. Add instant yeast and let activate briefly.

Add egg, melted butter, salt, and most of the bread flour to the mixture. Reserve 60 grams of flour for later.

Knead the dough for 8-10 minutes until smooth, adjusting with reserved flour as needed.

Place the dough in a bowl, cover, and let rise in a warm place for 1-2 hours.

Roll the risen dough into a 10 by 16-inch rectangle. Cut out about 12 4-inch donuts and 1-inch holes for donut holes.

Re-roll any dough scraps to make more donut holes or filled donuts.

Place cut donuts and holes on a parchment-lined baking sheet, cover, and let rise until doubled in size.

Heat coconut oil in an 8-inch saucepan to 350ºF. Monitor the temperature carefully.

Fry 2-3 donuts at a time for 1-2 minutes until browned. Flip and fry for an additional minute, then remove to a cooling rack.

Fry donut holes in batches for 2-3 minutes, stirring occasionally.

Whisk together powdered sugar, milk, vanilla extract, and salt for the glaze until smooth.

Dunk each donut into the glaze and top with sprinkles if desired.