In a saucepan, warm milk, sugar and butter over low to dissolve the sugar and butter.
Add mixture to a mixer with a dough hook, and 2 cups of flour. I like to do this to make sure the milk mixture has cooled down enough before adding my starter.
Add starter, eggs, the rest of the flour, and salt. Knead on low until smooth and elastic. This took about 10 minutes for my dough to finally come together and pull away from the sides.
Cover with a plastic wrap or beeswax wrap and leave in a warm place to rise for 5-6 hours.
Place dough in the fridge overnight.
The next morning, roll out on a lightly floured surface to ½″ thickness.
Cut the donuts out.
Place donuts on a sheet; cover with a damp tea towel or plastic wrap for 1.5-2 hours, depending on how warm the house is, to rise.
Add about ½ inch of oil to a cast iron skillet.
Heat the frying oil over medium heat until it sizzles when something is added.
Fry 2-3 minutes, flip, and fry another 2-3 minutes on the other side until puffy. Be careful not to overcrowd the pan.
Place on a wire rack over parchment paper to cool a little before glazing.
In a sauce pan - I like to use a slightly larger one to make dipping easier - add butter, milk, vanilla, and powdered sugar over low heat.
Heat, stirring occasionally until everything has melted and come together.
Turn off heat and set aside until ready to dip.
Dip the donuts in the glaze and set on wire rack to dry.