• Place the milk in a microwave safe bowl or measuring cup. Microwave on high in 30-second increments until the milk is warm but not hot.
• Add sugar to milk. Stir to dissolve. Add the yeast. Stir gently, then let sit for 10 minutes.
• In a small bowl whisk together the eggs and melted butter. In a separate bowl, whisk together the flour and salt. Set aside.
• Add the egg/butter mixture to the bowl of an electric mixer fitted with the dough hook. With the mixer on medium-low speed, pour in the yeast mixture. Allow the dough hook to stir this mixture for a couple of minutes, making sure it’s thoroughly combined.
• With the mixer still going, add helpings of the flour mixture in 1/4 to 1/2 cup increments until all the flour is gone.
• Stop the mixer, scrape the bowl, then turn the mixer on medium-low speed for five whole minutes.
• After five minutes, stop the mixer and scrape the bottom of the bowl. Turn on the mixer for 30 seconds.
• Turn off the mixer and allow the dough to sit in the bowl undisturbed for 10 minutes. After 10 minutes, transfer dough to a lightly oiled bowl. Gently turn the dough to coat, then cover the bowl with plastic wrap. 

To make the doughnuts the same day:

• Place the bowl in a warm place in your kitchen and let rise for about 1 hour, until doubled in size. If your kitchen is drafty, try placing the bowl in your oven with ONLY the oven light on (do not turn the oven on).
• Once doubled in size, proceed to making the doughnuts.

To make the doughnuts the next day:

• Place the bowl in the refrigerator. Refrigerate the dough for at least 8 hours, or overnight. The next day, proceed to making the doughnuts.

To Make the Doughnuts

• Gently turn out dough onto a lightly floured surface. Roll out to 1/4 to 1/3-inch thickness.
• Using a 3-inch cutter, cut as many rounds as you can, then roll out remaining dough and cut as much as you can, etc.
• Cut holes out of each round using a 1-inch cutter. If you have extra scraps of dough, use the 1-inch cutter to cut out extra doughnut holes.
• Place both doughnuts and holes on a floured baking sheet.
• Cover with a large tea towel and place in a warm place in your kitchen.
• Allow doughnuts to rise undisturbed for at least 1 hour; 1 hour 15 minutes if necessary. Doughnuts should be visibly puffier and appear to be airy.

To Fry the Doughnuts

• Heat at least 1 quart of canola oil in a large heavy-bottomed pot until the temperature reaches 375 to 380°F —do not let it get hotter than 380°F! 375°F is ideal; keep the thermometer in the pan to continually monitor and adjust your burner as necessary to maintain the temperature.
• One to two at a time, gently grab doughnuts and ease them into the hot oil. Allow them to cook 1 minute on each side; they will brown very quickly.
• Remove doughnuts from the oil with a slotted spoon, allowing all oil to drip off.
• Place doughnut immediately on several layers of paper towels. Count to five, then flip it over onto a clean part of the paper towels. Count to five, then move the doughnut to a wire rack set over a rimmed baking sheet.
• Repeat with remaining doughnuts and holes. The holes will cook more quickly than the doughnuts; about 30 seconds per side.
• Allow doughnuts to slightly cool.

To Glaze

• Mix all glaze ingredients in a bowl until completely smooth.
• One by one, dip doughnuts into the glaze until halfway submerged. (Note: completely submerge doughnut holes, then remove with a slotted spoon.)
• Remove from glaze, then return them right-side up to the wire rack still set over the rimmed baking sheet. The baking sheet will catch any excess glaze that drips off. 
• Serve warm if possible, or room temperature.