For the Doughnuts:
- 2 teaspoons warm water (about 105 degrees)
- 1 (¼-ounce) package active dry yeast (2¼ teaspoons)
- 3 1/2 to 3¾ cups all-purpose flour, plus more for rolling
- 1 cup whole milk, at room temperature
- ¼ cup (½ stick) unsalted butter, at room temperature
- 3 large egg yolks
- 2 tablespoons sugar
- 1½ teaspoon salt
- ¼ teaspoon ground cinnamon
- 6 cups vegetable oil, for frying
For the Cranberry Jam:
- 1 12-ounce bag fresh cranberries
- 1/2 cup granulated sugar
- 1/2 cup water
- pinch of salt
- 2 orange peel slices
For the Orange Sugar:
- 1 1/2 cups granulated sugar
- 2 teaspoons orange zest
- 1 teaspoon ground cinnamon
- 1/2 teaspoon freshly grated nutmeg
- 1/4 teaspoon ground cloves
- 1/4 teaspoon ground allspice
- To make the doughnuts, in a small bowl, stir together the warm water and yeast until the yeast is dissolved. Let stand until foamy, about 5 minutes. (If the yeast doesn’t foam, discard and start over with new yeast.)
- In the bowl of an electric stand mixer fitted with a dough hook, combine the yeast mixture, flour, milk, butter, egg yolks, sugar, salt, and cinnamon. Beat at low speed until a soft dough forms. Increase the speed to medium-high and beat 3 minutes more. The dough will be soft and sticky. If it’s too sticky to handle, add up to ½ cup more flour.
- Scrape the sides of the bowl and then lightly sprinkle the dough with flour (to keep a crust from forming). Cover the bowl with plastic wrap and a clean kitchen towel. Put the bowl in a warm place and let the dough rise until doubled in bulk, 1½ to 2 hours.
- To make the cranberry sauce, in a medium saucepan combine cranberries, sugar, water, salt, and orange peel. Bring to a simmer and reduce heat to low and the cranberries pop and cook down. Simmer for 10 minutes, until berries have broken down and sauce has thickened. Remove from the heat and remove orange peels. Set aside until doughnuts are fried.
- To make the spied sugar, spread the sugar on a small rimmed baking sheet. Add the orange zest and spices and use your fingers to work the zest into the sugar, creating a fragrant sugar. Set aside until the doughnuts are fried along with the cranberry sauce.
- Dump the dough out onto a lightly floured counter. Using a lightly floured rolling pin, roll the dough out into a 12-inch round that’s ½ inch thick. Cut out as many rounds as possible with a 3-inch cutter (or a doughnut cutter, if you prefer a hole in the middle) and transfer the doughnuts to a lightly floured baking sheet. Do not reroll scraps (they’ll make for tough doughnuts). Cover the doughnuts with a clean kitchen towel and let rise in a warm place until slightly puffed, about 30 minutes.
- Heat 2½ inches of oil in a deep, 4-quart, heavy pot until it registers 350 degrees on a thermometer. Fry the doughnuts, 2 at a time, turning occasionally, until puffed and golden brown, about 1 minute per side. Quickly submerge the doughnuts in the hot oil, and then immediately transfer them to the spiced sugar Toss well, transfer to a cooling rack and allow to cool.
- Return the oil to 350 degrees between batches and continue until all of the doughnuts are fried.
- Use the back of a spoon to make a small hole in the top of each sugar-coated doughnut. Spoon a heaping tablespoon of cranberry jam into each doughnut.
- Doughnuts are best served the day they are made. Enjoy them generously.