Activate Yeast Mixture:

In a small bowl, whisk together the yeast, milk, and 2 Tbsp of the sugar. Let stand for 10-15 minutes until foamy.

Mix Dough Base:

In the stand mixer bowl with the dough hook, combine the flour, salt, and remaining 2 Tbsp sugar. Mix briefly. Add the eggs, vanilla, and the foamy yeast mixture. Mix on low for 2-3 minutes until dough begins to come together (it may seem a bit dry). Then increase to medium and mix for 10 minutes until soft and smooth.

Incorporate Butter:

Reduce speed to low and incorporate the butter piece by piece, waiting until each addition is fully absorbed (3-4 minutes total). Once all butter is added, increase to medium and mix for 5 more minutes until the dough is very soft and smooth.

Chill Dough Overnight:

Move the dough to a greased bowl, cover tightly with plastic wrap, and chill overnight in the refrigerator (see notes).

Roll Dough Thick:

Prepare two sheet pans with parchment paper squares. On a well-floured surface, roll the dough to a thickness of 1/2-inch (1.25 cm).

Cut Doughnut Shapes:

Using a 1 3/4-inch (4.5 cm) round cutter, stamp out circles. With a very small round cutter or a milkshake straw (I used a metal bubble tea straw), punch a hole in the middle of each. Arrange on the parchment squares (several per sheet). Repeat with all dough; press scraps together and re-roll. Use scrap doughnuts for the first test fry as they may be irregular.

Proof Shaped Doughnuts:

Loosely cover the shaped doughnuts with plastic wrap and allow to rise for 45-50 minutes until puffy. When lightly poked, a small indentation should remain and slowly spring back.

Heat Oil and Mix Sugar:

During the last 15-20 minutes of proofing, heat neutral oil to 350°F (175°C) in a large heavy-bottomed pot (cast iron works great) or deep fryer. The oil depth should be enough for doughnuts to float. Set a wire rack over a parchment-lined baking sheet. In a medium bowl, stir together the granulated sugar and cinnamon.

Fry and Coat Doughnuts:

Once oil is at temperature, test with a few dough scraps or re-rolled doughnuts. Carefully lower up to 6 doughnuts at a time into the hot oil. Fry, turning every 30 seconds, for 3-4 minutes until golden brown. Remove with a slotted spoon and transfer to the cooling rack. Let cool for 30 seconds, then toss in the cinnamon sugar mixture. Repeat with remaining doughnuts.

Store and Reheat:

Best consumed on the day they are made. Store leftovers in an airtight container and briefly reheat in the microwave.