Sourdough Raised Donuts

Steps

1. 1Prepare tangzhong mixture: Whisk together 180g milk and 38g flour in a small saucepan over medium heat. Cook and stir constantly with a rubber spatula until the mixture thickens to the consistency of mashed potatoes. Cover and allow to cool completely. (To speed up cooling, spread mixture flat on a large dinner plate and cover the surface with plastic wrap. Refrigerate until completely cool.)
2. 2Mix dough: To a stand mixer fitted with a dough hook (and dough hook extender if using a Bosch mixer), add cooled tangzhong, ripe starter, eggs, sugar, flour, and vanilla extract. Mix on low speed for 1 minute until combined. Cover dough and allow to rest for 30 minutes. Add salt and knead for 10 minutes on low speed. At this point, the gluten should be mostly developed. Add half the butter cubes and continue kneading until butter is thoroughly incorporated and no longer visible. Repeat to knead in the second half of the butter cubes. Access the dough at this point: if it's very smooth, taught, and shiny, cleans itself off the sides of the bowl to cling to itself and the dough hook and stretches to a dramatic windowpane when pulled with damp fingers, it's done. If it doesn't yet show these signs, continue kneading until it does (even if it takes 10-15 more minutes).
3. 3Warm bulk ferment and refrigerate overnight: With damp hands, form dough into a smooth ball. Place dough in a large bowl or straight-sided container. Cover and set in a warm place until it has nearly doubled in size (approximately 2 hr, 45 min with a final dough temp of 76°F and an ambient temp of 78°F. Bulk will take longer if your dough/kitchen are cooler). After the dough has risen, cover tightly and refrigerate overnight.
4. 4Roll and cut donuts: The next day, line two half sheet pans with six 5-inch squares of parchment paper on each. Lightly dust parchment paper squares with flour. Turn out cold dough onto a clean countertop and roll evenly to 1/2-inch thickness (avoid handling dough more than necessary). Insure rolled dough is not sticking to the counter, then use a 3-inch donut cutter to cut donuts as closely spaced as possible. Place donuts on prepared pans, one donut on each square of parchment. (Scraps do not re-roll well. You can re-roll scraps once to cut a couple more donuts, then discard remaining scraps or use for another purpose. Donut holes may be proofed on a separate tray and fried, if desired.)
5. 5Proof: Cover pans with plastic wrap and set in a warm place to proof until donuts are very puffy with air and soft to the touch (they may pass the poke test a little before being fully proofed). You should see some visible air bubbles inside the center holes (about 3 hrs, 20 min at 76-78°F, longer if your kitchen is cooler).
6. 6Fry: When donuts are nearly proofed, fill a heavy-bottomed pot with 2 inches of frying oil. Set over medium heat with a candy thermometer clipped to the inside edge. Line a cooling rack with a double layer of paper towels and set near frying pot. Begin frying when oil reaches 360°F. Fry only 3 or 4 donuts at a time (see notes for signs of proper proofing when frying). Fry on the first side until golden brown, then flip to fry the second side, about 2 minutes per side. Maintain proper oil temp before repeating to fry remaining donuts. (The parchment squares will allow you to gently transfer the donuts to the pot without deflating them. If the donuts won't release while inverting, simply fry them with the parchment. The parchment will release and can be carefully removed from the frying oil with kitchen tongs into a bowl held over the oil.) Remove fried donuts from oil with a spider strainer spoon and transfer to the paper towels to drain and cool.
7. 7Glaze: While donuts are cooling, prepare desired glaze. Add powdered sugar, (cocoa powder for chocolate glaze), whole milk, melted butter, vanilla, and a pinch of salt into a small bowl. Whisk briskly until glaze is very smooth with no lumps. Cover and set aside. Once donuts have cooled completely, dip them into the glaze to coat the tops. Place donuts glazed-sides-up on a cooling rack or sheet pan, uncovered for about 20 minutes, until glaze is set (vanilla glaze will run down the sides of the donuts). Serve.