• In a small bowl, whisk together the warm milk, yeast, and 1 teaspoon of sugar. Let it sit for 5 to 10 minutes, until the surface looks foamy and smells slightly yeasty.
  1 ¼ cups warm whole milk 110°F, 2 ¼ teaspoons active dry yeast, 1 teaspoon granulated sugar for yeast activation
• In the bowl of a stand mixer fitted with the dough hook, combine the remaining ¼ cup sugar, softened butter, eggs, and egg yolks. Mix on medium speed until the mixture looks smooth and creamy—it’s okay if a few small butter pieces remain. Add the activated yeast mixture and mix until combined.
  ¼ cup granulated sugar, ½ cup unsalted butter softened, 2 large eggs room temperature, 2 large egg yolks room temperature
• Add the flour and salt, then mix on low speed until a soft dough starts to form. Increase to medium speed and knead for 8 to 10 minutes, or until the dough is smooth, elastic, and slightly tacky but not sticky. The dough should pull away from the sides of the bowl and feel soft and stretchy when pressed with your fingertip. If it feels too sticky, add a tablespoon or two of extra flour as needed.
  5 ⅓ cups 725 g bread flour or all-purpose flour plus extra for rolling spooned and leveled, 2 teaspoons salt
• Transfer the dough to a lightly greased bowl, turning once to coat. Cover tightly and refrigerate for at least 6 hours, or up to 12 hours. The slow rise adds flavor and makes the dough easier to work with.
• After chilling, the dough will feel firm from the cold butter—that’s normal. If it’s too stiff to roll, let it rest on the counter for 10 to 15 minutes before rolling. Turn the dough out onto a lightly floured surface and roll it into a large rectangle about ½ inch thick, roughly the height of two stacked quarters.
• To cut the donuts, use a sharp knife, bench scraper, or pizza cutter to cut the dough into even bars, about 4 to 5 inches long. Press straight down instead of dragging to keep the edges clean. Use a small offset spatula or bench scraper to carefully lift each bar and transfer it to a parchment-lined baking sheet, spacing them a few inches apart.
• Cover the baking sheet lightly with plastic wrap or a clean kitchen towel and let the donuts proof at room temperature for about 2 hours, or until they’re noticeably puffy and spring back slowly when gently pressed with a fingertip.
• When ready to fry, heat the lard or canola oil in a large heavy-bottomed pot or Dutch oven to 325°F. Fry the donuts in batches, about 1 to 2 minutes per side, until they’re puffed and deep golden brown. They should float almost immediately when they hit the oil, and the bubbles around them should stay gentle rather than furious—that’s how you know your oil temperature is right.
  2 cups lard or canola oil
• Use a slotted spoon to transfer the fried donuts to a paper towel–lined tray to drain. Let them cool for 5 to 10 minutes before glazing so the brown butter maple glaze clings beautifully without melting off. While the donuts cool, make the glaze.

For the brown butter maple glaze:

• Add the butter to a medium saucepan and melt it over medium heat. Once melted, continue cooking, swirling the pan often. The butter will foam, then the foam will start to subside as brown specks form on the bottom. Keep a close eye—it can go from browned to burnt quickly. When it smells nutty and caramel-like and turns a deep golden color, remove it from the heat immediately. This should take about 5 to 7 minutes total.
  6 tablespoons unsalted butter
• Let the browned butter sit for about 2 to 3 minutes to cool slightly.
• Whisk in the powdered sugar, salt, maple extract, and pure maple syrup until the mixture comes together. It will be thick at first.
  4 cups powdered sugar, ¼ teaspoon salt, ½ teaspoon maple extract, ½ cup pure maple syrup
• Add milk, 1 tablespoon at a time, whisking after each addition until the glaze is smooth, glossy, and pourable. It should drip slowly from the whisk and coat a spoon in a thin, even layer.
  3-4 tablespoon milk
• Use the glaze right away for the best shine. Drizzle it over the cooled donut bars or dip the tops directly into the warm glaze for a bakery-style finish.