Add yeast to warm milk in a bowl and let it activate for 5 minutes until it is frothy.
Next, add the sugar, salt, eggs, and butter, and mix until well combined.
Mix in the flour one cup at a time.
Knead the donut dough on a lightly floured surface until it's smooth and elastic (about 5 minutes). Or, for an easier way, do it in a stand mixer with the dough hook.
When the dough is ready, place it in a large, greased bowl, then cover it and let it rise for an hour. It should double in size.
Punch down the dough and turn it onto a lightly floured surface.
Roll the dough into a ½-inch-thick rectangle. Then, using a donut cutter or 3½-inch and 1½-inch round cookie cutters, cut out the donuts and holes.
Place the cutouts on the prepared baking sheet as you work. Cover the donuts loosely and let them rise in a warm place for 20 minutes.
Place the cutouts on the prepared baking sheet as you work. Loosely cover and let rise in a warm place for 20 minutes.
Heat oil (about 2 inches) in a Dutch oven until a deep-fry thermometer registers 350℉/177℃.
Fry your donuts in the hot oil until a beautiful golden brown (it takes about 1 minute per side for large donuts), then transfer them to the wire rack to drain.
Make your glaze by mixing powdered sugar, melted butter, vanilla extract, and milk in a bowl until well combined.
Dip the warm donuts into the glaze, coat both sides, and place them on the wire rack.
Enjoy them warm with a fresh, hot cup of coffee or tea.