In a bowl fitted for a stand-mixer, add warmed milk, flour, yeast, salt, sugar, and eggs. Attach dough hook and mix ingredients on low for 2 minutes until all the ingredients are combined, scrapping down the sides, as needed, to incorporate all the ingredients. Once incorporated, continue mixing for another 2-3 minutes until the dough smooths out.
Cut butter into 7 pieces. Add one piece of butter to dough and mix on low until completely incorporated into dough. Repeat with remaining pieces of butter, 1 piece at a time. Once all butter is added, continue to mix on low for another 5 minutes. It is important for all the butter to be thoroughly mixed into the dough. If the mixture is too loose, add more flour a couple tablespoons at a time until it slightly separates from the bowl.
Put the dough in a large bowl or plastic container and cover it with plastic wrap, pressing the wrap directly onto the surface of the dough to prevent it from drying out. Let the dough proof in the refrigerator overnight (16 hours max).
The next morning, prepare a baking sheet by dusting with flour. Set aside. Unwrap the dough and place onto floured surface. Roll out the dough until it's about 1/2 inch thick. Cut out doughnuts with a round cookie cutter about 3 inches in diameter and place onto floured baking sheet. Combine scraps and rolls it out again and cut out more doughnuts until all the dough is used.
Cover doughnuts with plastic wrap and place in a draft-free place to proof for 1.5 hours.
When there's 15 minutes left of proofing time, add oil to a Dutch oven and heat over medium heat until the temp reaches 360 degrees. Use a candy thermometer to monitor the temp because it's super important.
Once the oil is hot, add 3-4 doughnuts to the oven and cook for 2 minutes, flip and cook for 2 more minutes. The outside will get super brown but I promise they are not burning. Remove doughnuts and place on paper towels to drain off the extra oil. You can double-check if they're done cooking by using a thermometer. Make sure the center has reached 190 degrees. If not, place back in oil to cook a little more. Repeat with the rest of the doughnuts.