Heat milk, sugar, and butter in a small saucepan or microwave-safe container just until the milk warms and the butter melts. When mixing with sourdough starter, ensure the mixture is warm, not hot, to avoid destroying natural yeast.  

Combine the milk mixture, sourdough starter, salt, and eggs in a stand mixer, then mix on low speed until combined. 

Add 2 ½ cups of the flour then using a dough hook, knead on medium-low speed for 4-5 minutes to form a tacky dough. Allow dough to rest for 10 minutes, then add a tablespoon or so of flour and knead for another 4-5 minutes.  

Transfer dough to a floured surface, kneading by hand until it is no longer sticky, forming a smooth elastic ball.  

Place dough in a greased bowl, covering with a damp kitchen towel or plastic wrap to rise for 3-6 hours or until dough doubles in size at room temperature.  

Roll out dough on a floured surface, using a donut cutter or circular cutter, and stamp out donuts and donut holes.  

Place cut-outs on a flat surface, letting rest for 1 hour to become slightly puffy.  

Preheat oil in a deep pan or Dutch oven to 350ºF  

While the oil is pre-heating, mix all the glaze ingredients to create the sugar glaze.  

Fry the donuts for 1½ minutes per side, then remove them to a paper towel. Once dry, transfer them to a baking rack over a sheet pan.