I have never made sourdough doughnuts before so I did a google search and came up with this from Baking Sense. I added some ginger and lemon to this recipe and came up with my own filling.
1 cup whole milk, warmed to about 120°F
1 large egg (room temp)
4 tablespoons unsalted butter, melted
224g active sourdough starter
3 1/2 cups unbleached all-purpose flour
1/2 cup granulated sugar for dough + 1 cup for rolling after frying
2 teaspoons ginger
Zest of one lemon
Zest of one orange
1 teaspoon table salt
Canola Oil for frying
1 cup sugar
1/4 cup unsalted butter, room temperature
1/2 cup fresh squeezed orange juice
1/4 cup fresh squeezed lemon juice
1 tablespoon orange zest
1 tablespoon lemon zest
2 large eggs, beaten
1 cup heavy whipping cream
1/4 teaspoon salt
Make the Dough (Day 1)
Combine the warm milk, butter and egg with the starter in a mixer bowl. With the mixer running, add sugar, spices, salt and 2.5 cups of the flour. Mix until it forms a thick batter.
Switch to the dough hook and add the remaining flour (amount of flour may vary based on the hydration of your starter). The dough will start out quite sticky. Knead on medium low speed for 15 minutes (speed 2 on my stand mixer) until the dough clings to the hook and clears the sides of the bowl.
Scrape the dough into a lightly floured surface and knead into a smooth ball. Place the dough into a lightly oiled bowl, turning once to coat the dough. Cover and set the dough aside at room temperature for 4-5 hours.
Every hour repeat the following procedure: Uncover the bowl, lift one edge of the dough over into the middle of the dough. Repeat with the other three sides of the dough then flip the dough over. Cover the bowl and set aside. By now the dough should be lively, elastic and airy. If the dough is still sluggish give it another hour or two at room temperature. Cover and refrigerate overnight.
Make the filling
To prepare the filling, create a double boiler by bringing a pot of water to boil and placing a heat-proof mixing bowl on top.
Whisk in lemon juice, zest, sugar and eggs. Continue whisking on the double boiler until it starts to thicken slightly. Drop butter into the mixture one tablespoon at a time.
Once the butter has been added, continue whisking until it is thick enough to coat the back of a spoon.
Remove from heat, and place in the refrigerator for at least an hour, or until it has cooled completely.
Meanwhile, in a mixing bowl whisk heavy cream and salt together until it forms stiff peaks. Carefully fold in the cooled lemon mixture. Place in the refrigerator for at least another 30 minutes. or overnight.
Remove the dough from the refrigerator. While the dough is still cold, without kneading, roll to 1/2″ thick on a lightly floured surface.
Use a 4″ round cutter to cut donuts. Line the donuts on a well-oiled, parchment or silpat lined baking sheet, leaving space between the donuts for the dough to rise. Re-roll the scraps of dough and continue cutting donuts until all the dough is used up. Brush the tops of the donuts lightly with oil.
Cover the sheet pans with plastic wrap and set aside to rise. The donuts are ready when you poke the dough and the dent slowly fills in. If the dough bounces right back it’s not quite ready. This rise should take about 1 1/2 hours. The time will vary based on the temperature of the room.
Meanwhile, heat 2 quarts of oil to 350F° in a large heavy pot. Fry the donuts a couple at a time, about 2-3 minutes per side, until golden brown and puffy.
As you take each donut out of the oil, immediately roll in sugar to coat the entire donut. Set on a cooling rack while you fry the rest of the donuts. You need to let them cool before you fill them.
Right before serving, cut small holes in the side of each doughnut with a paring knife, in the shape of an X. Place filling in a piping bag fitted with a piping tip. You will feel the doughnut expand when full. Enjoy immediately. No one likes an old doughnut.