Glazed Yeast Donuts

Lemon Confectioners'-Sugar Glaze: Whisk together confectioners' sugar and salt. Whisk in juice until mixture is smooth and thick, and has the texture of pourable honey. Glaze can be refrigerated in an airtight container up to 3 days; stir until smooth before using. (Makes 1 1/2 cups.)

Donuts: Whisk together flours. Combine water and milk in the bowl of an electric mixer fitted with the dough-hook attachment, then sprinkle yeast over top. Stir in 1 cup flour mixture. Cover with plastic wrap; let stand in a warm place until bubbling and doubled in volume, about 1 hour. Add egg and yolk, granulated sugar, salt, and remaining flour mixture. Beat on medium speed 3 minutes. Continue beating while adding butter, a few pieces at a time, beating to combine after each addition. When all butter has been added, keep beating until a shiny, sticky dough forms around hook, about 4 minutes more. Scrape down sides of bowl.

Cover dough with plastic wrap. Let stand in a warm place until almost doubled in volume, about 1 hour. Refrigerate at least 8 hours and up to 24.

Cut out 24 three-inch squares of parchment. Spray two baking sheets with oil; arrange parchment squares in a single layer on them. Spray parchment. Transfer dough to a lightly floured baking sheet; pat out 1/2 inch thick. Using a floured 2 1/2-inch donut cutter, cut out donuts (or use a 2 1/2-inch cookie cutter to cut out rounds, then cut out holes with a 1-inch round cutter). Transfer to parchment squares. Drape with oil-sprayed plastic wrap and let stand in a warm spot until slightly more than doubled in bulk and very soft, about 1 hour.

Meanwhile, pour oil into a large, deep, heavy pot, such as a Dutch oven, until it reaches 2 inches up side, leaving about 2 1/2 inches headroom. Clip a deep- fry thermometer to pot and heat oil over medium to 350 degrees to 360 degrees. Working in batches of 3 so as not to crowd pot, carefully use parchment to transfer donuts to hot oil and cook, flipping a few times, until puffed and golden brown all over, 2 to 3 minutes total for donuts (1 1/2 to 2 minutes for holes), maintaining oil temperature between 350 degrees and 360 degrees at all times. Transfer donuts to a wire rack set in a rimmed baking sheet; let cool 10 minutes.

While still slightly warm, dip top of each donut in glaze until halfway submerged, turning as needed to evenly coat one side, then place, glaze-side up, on rack. Let stand until glaze sets and donuts are cool, about 1 hour.