Activate the yeast

• Pour the warm milk into a large bowl.
• Add part of the granulated sugar and sprinkle the yeast overtop.
• Stir and let sit until frothy and activated.

Mix the dry ingredients

• In a large bowl, whisk together the flour, salt and cinnamon.

Start the dough

• Pour the activated yeast mixture into the bowl of a stand mixer.
• Add the remaining sugar, the eggs, the melted butter, the vanilla and half of the flour mixture.
• Mix on low speed with the dough hook until barely combined.

Rest the batter

• Let the mixture rest so the flour can soak up the liquids.

Knead the dough

• Add the rest of the flour mixture and mix on medium speed until the dough is elastic, smooth and pulling away from the sides of the bowl.
• If the dough is too sticky, add a little more flour at a time, keeping it slightly sticky.
• By hand: mix in the flour, turn onto a floured surface and knead.

First rise

• Transfer the dough to a lightly oiled bowl, cover and let rise in a warm place until doubled in size.

Prepare the parchment squares

• Cut out squares of parchment paper and spread them over two baking sheets.
• Lightly dust each square with flour.

Shape the donuts

• Punch down the dough and turn it onto a lightly floured surface.
• Roll the dough out to about 1/2 inch thickness.
• Cut out the donuts with a donut cutter, cup or jar lid, then cut out the holes in the middle with a smaller cutter or the wide end of a piping tip.
• Place the donuts on the floured parchment squares.

Proof the donuts

• Loosely cover the donuts with a kitchen towel and let them proof until puffy.

Make the cinnamon sugar

• Mix together the granulated sugar and cinnamon in a medium bowl.

Heat the frying oil

• Fill a large heavy-bottomed pot or Dutch oven with oil to about 2 inches deep.
• Heat on medium-high until it reaches 360-375 °F.
• Line a wire cooling rack with a thick layer of paper towels.

Fry the donuts

• Carefully slide the parchment squares with the donuts into the hot oil, a few at a time.
• After a few seconds, pull the parchment paper away from the donuts.
• Fry on each side until deep golden brown, then remove with a slotted spoon onto the paper towels.

Coat and serve

• Dip the warm donuts into the cinnamon sugar, rolling to coat.
• Serve warm, ideally with a hot cup of coffee.