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Heat the milk until it is warm TO TOUCH and in 1/2 cup of milk combine sugar and the yeast. Stir lightly, and let sit until the mixture is bubbly or when foam starts to foam, about 5 minutes. This means that the yeast is active and ready.
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Mix 2 eggs in the remaining warm milk to warm them up and set aside.
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In a large bowl add flour, salt, and sugar. Stir to combine, then make a well in the middle.
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First, add activated yeast in the well, then mixed eggs and milk. Using a spatula or a wooden spoon, mix everything together. When everything is combined, knead the dough for about 10 minutes. You may use a stand mixer with hook attachment if you find that easier.
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Let rise at room temperature until it doubles in size, about 1 hour, or up to 3 hours.
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Turn the dough out onto a well-floured surface, and roll it to 1/2-inch thickness. Cut out the doughnuts with a doughnut cutter, or a glass and a shot glass, flouring the cutters as you go. Reserve the doughnut holes. (If you’re making filled doughnuts, don’t cut out the middle. Knead any scraps together, being careful not to overwork, and let rest for a few minutes before repeating the process)
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Put the doughnuts on two floured baking sheets to rise before frying. Cover with a kitchen towel, and let rise in the room temperature until they are slightly puffed up about 20-30 minutes.
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About 15 minutes before the doughnuts are done rising, put the oil in a heavy-bottomed pot over medium heat, and heat it to 375 Fahrenheit. Meanwhile, prepare cooling cookie racks, or large plates with kitchen paper towels.
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Carefully add the doughnuts to the oil, a couple at a time. Don't overcrowd the pot.
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When the bottoms are deep golden, after 45 seconds to a minute on one side, use a slotted spoon or two large forks to flip; cook until they’re deep golden all over. Transfer the doughnuts to the prepared cookie rack or a large plate lined with kitchen paper towel, and repeat with the rest of the dough, adjusting the heat as needed to keep the oil at 375 Fahrenheit. Glaze or fill your donuts, and serve as soon as possible.
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I like using sugar and cinnamon powder, or sugar infused with vanilla flavor. If they are without a hole, then I like filling them with Nutella or jam.