Heat the milk and butter in a small saucepan or microwave-safe container just until the milk is warm and the butter is melted. If it gets overly hot, let it cool before the next step.
Add the milk and melted butter, active sourdough starter, eggs, 3 cups flour, and salt to the bowl of your stand mixer and mix it with the paddle attachment for a minute, until it looks smooth.
Switch out the paddle attachment for the dough hook, and add the remaining 2 cups of flour. Start mixing on low speed until the flour is incorporated, and then turn up to medium speed and let it mix for 4 minutes. The dough should come together into a smooth ball, and the sides of the bowl should be free of dough. If it looks too wet and sticky, add ¼ cup of flour.
Transfer the dough from the stainless bowl to a greased large bowl, allowing it to double in size over the next couple of hours.
Cover the dough with a lid or a damp towel and let it rise for about 6 hours at room temperature. This will vary depending on the temperature of your home, but you will know when it has almost doubled in size and is ready.
Place the donut dough on a clean surface and roll it out to about ½ inch thick. If it's too sticky, roll it on a lightly floured surface or use a tiny bit of oil on your hands.
Using a donut cutter, cut your donuts and donut holes.
Place the cut-out donut holes on a well-oiled piece of parchment paper and let them rest for 1 hour.
Meanwhile, prepare your glaze (recipes below).
When your dough has rested for an hour and the donuts look slightly puffy, prepare your frying oil. You can use a fryer or whatever frying method you prefer and set it to 325 degrees F. I add an inch of coconut oil to a deep frying pan on my stove and use a food thermometer to know when the oil temperature reaches 325 degrees F. You want to keep it at a consistent temperature.
Add a few donuts to the oil at a time, and leave for one minute or until the bottoms have turned a golden brown. Flip the donuts and heat the other side until they are golden brown as well.
Transfer the cooked donuts to a cooling rack lined with paper towels to soak up excess oil.
Before the donuts are cooled, dip them into the prepared glaze and place them back onto the cooling rack, where they will finish cooling and the glaze will set.
Serve your donuts fresh for the best crispy results.