Stir together yeast and warm water in a small bowl until yeast is dissolved. Let stand until foamy, about 5 minutes. (If yeast doesn’t foam, discard and start over with new yeast.)
In the bowl of a stand mixer fitted with a dough hook, combine flour, milk, butter, yolks, sugar, salt, cinnamon, and yeast mixture. Use a spatula to quickly bring the ingredients together then mix at low speed until a soft dough forms. Increase speed to medium-high and beat 3 minutes more.
Scrape dough down side of bowl (all around) into center, then sprinkle lightly with flour (to keep a crust from forming). Cover bowl with plastic wrap and let dough rise in a draft-free place at warm room temperature until doubled in bulk, about 1 hour.
Turn dough out onto a very lightly floured surface. You won’t need much flour at all because you want the dough to stick to the counter just a bit. The resistance helps the top elongate and the doughnut twist stick to itself and stay coiled during frying.
Divide the dough in half.
Roll each half of dough into a 15-inch rope. Fold the rope in half, creating two 7 1/2-inch strands parallel from one another. Twist the dough ropes over each other, creating a twist, pressing and folding the two strands of dough together and under to seal the doughnut. Repeat with the second half of the dough.
Place the two twisted doughnuts on a parchment lined baking sheet. Allow to rise for 30 minutes.
While the doughnuts rise, mix together sugar, cinnamon, and salt in a bowl large enough to toss around the cooked doughnut.
When you’re ready to fry the doughnuts, place 1 qt of oil into a 3 qt saucepan. Attach a candy thermometer to the side of the pan so that the bulb is submerged in the oil to register the temperature. Heat over medium-high heat until the oil reaches 355 degrees F.
Fry one doughnut at a time.
Gently lower the doughnut into the hot oil and allow to fry and brown for 30 – 45 seconds. Flip to the other side and fry for 30 – 45 seconds more. Rotate the doughnut through the oil for 15 more seconds, making sure that every bit of the doughnut is moistened with very hot oil. Remove and quickly transfer to the cinnamon and sugar mixture. Quickly toss to coat on all sides and remove from the sugar and place on a wire rack.
Return oil to 355°F between batches and fry second doughnut. Quickly transfer to sugar mixture, coat generously and allow to rest on the wire rack.