In the bowl of a stand mixer, combine the warmed milk, yeast, and sugar. Let the mixture sit for 5 minutes to activate the yeast. Whisk in the egg until fully incorporated. In a separate large bowl, whisk together the flour and salt. Attach the dough hook to your stand mixer. With the mixer on low speed, add one-third of the flour mixture to the wet ingredients. Once the dough begins to come together, add another third of the flour mixture. Then, add the softened butter one tablespoon at a time, mixing well after each addition. At this stage, the dough will be sticky. Scrape down the sides of the bowl as needed to ensure even mixing. Add the remaining flour mixture.

When the dough starts to form, increase the mixer speed to medium and knead for 3 to 5 minutes until the dough becomes smooth and soft. The dough may still cling slightly to the sides of the bowl but should be easy to scrape off with a spatula or dough scraper. Avoid adding any extra flour. Transfer the dough to a large greased bowl, cover it with plastic wrap or a kitchen towel, and allow it to rest at room temperature for 30 to 45 minutes, or until it has doubled in size.

Once risen, gently deflate the dough and transfer it to a lightly floured surface. Divide the dough into 12 equal portions and loosely cover with a kitchen towel. Take one piece at a time and stretch and roll it into a 14-inch long strip. To form the twist, hold the ends of the dough rope with your hands, then roll one hand upward while rolling the other downward simultaneously. This action twists the dough naturally. Pick up the twisted rope by the center—the tension will cause it to braid together. Pinch the ends to seal and place each twisted doughnut on a parchment-lined baking sheet. Loosely cover with a kitchen towel and repeat the process with the remaining dough pieces.

Allow the shaped doughnuts to rest for 8 to 10 minutes while heating the oil. Attach a kitchen thermometer to a heavy-bottomed pot, such as a Dutch oven or cast iron pan, and fill it with 2 to 3 inches of vegetable oil. Heat over medium heat until the oil reaches 350°F. Carefully add two or three doughnut twists to the hot oil, making sure not to overcrowd the pot. Fry for about 95 seconds on each side until golden brown. Remove the cooked doughnuts with a slotted spoon and drain them on a paper towel-lined baking sheet.

Note that the oil temperature will drop when you add the doughnuts; keep an eye on the thermometer to maintain the correct temperature and prevent the doughnuts from burning or cooking unevenly.

For the cinnamon sugar coating, combine granulated sugar and ground cinnamon in a shallow dish and set aside. While still warm, toss the fried doughnuts in the cinnamon sugar until fully coated. Serve immediately and enjoy!