Doughnut time! Combine yeast, warm milk, and 2 teaspoons sugar in a large bowl of a stand mixer and stir to dissolve. Wait 10 minutes, the mixture should get foamy. If it doesn’t the milk was probably too hot, too cold or the yeast is dead. Try again!
To the yeast mixture, add 3¼ cups flour, remaining sugar, cinnamon and stir to combine. Add eggs, one at a time, and mix with the dough hook until dough starts to come together. Then add salt and combine.
With the mixer on low, add butter, a little at a time, until it’s incorporated into the dough. Then, mix on medium speed for about 5 to 10 minutes until dough is completely smooth and shiny. Make sure to scrape down the sides as you mix so everything gets incorporated.
Knead dough on a floured surface until slightly tacky but no longer sticky, adding more flour if needed, about 5 minutes. Coat a large bowl with oil and place dough inside. Let rise in a warm place until doubled in size, about 2 hours. You can also slow rise in the refrigerator for 12-24 hours.
When the dough is ready, punch it down and transfer to a lightly floured surface. (Bring to room temperature if doing the slow rise. Roll dough out to ¾-inch thick and cut out doughnuts using a 3-inch round cutter. Roll out scraps to make more doughnuts.
Place doughnuts on parchment paper–lined baking sheets about 1 inch apart. Cover loosely with plastic wrap and let rise in a warm place until they puff up, about 1 hour. At this point, you can refrigerate them for up to 2 hours if you’re not ready to fry them. Bring to room temperature before frying.
Time to make the filling!
In a medium bowl, beat cream cheese with electric beater until light and fluffy. Then add confectioner's sugar and molasses and beat until smooth. Add in spices and enough eggnog until you have the desired consistency. Place in a piping bag.
To make the drizzle, whisk together confectioner's sugar and enough eggnog to make it runny but thick.
When ready to fry, heat 2 inches of oil in a heavy-bottomed pot until it reaches 350 degrees. Working in batches and being careful not to overcrowd the pan, fry the doughnuts. Flip them halfway through until both sides are golden brown, about 1–2 minutes per side. Let cool on cooling rack.
When doughnuts are cool enough to touch, poke a hole in the top using the tip of the pastry bag. Fill with gingerbread filling until doughnut has some heft to it and drizzle with eggnog drizzle and garnish with crushed candy cane. Eat!
Tip: Doughnuts require deep-frying. Don’t freak out! Invest in a deep-fry thermometer to keep track of the temperature and make sure you roil isn’t getting too hot. Keep your frying station clean and dry—you don’t want any rogue kitchen tools or ingredients falling in the oil.