In a small bowl, stir together the lukewarm water, yeast, and 1 tablespoon sugar. Let sit for 10 minutes, until foamy and active on top. If it does not foam, start again.
In the bowl of a stand mixer fitted with the dough hook, whisk together the flour, 50 grams sugar, dry milk powder, and kosher salt. Add the whisked eggs, melted butter, room temperature milk, and the yeast mixture.
Mix on low until a shaggy dough forms, then increase to medium-low and knead for about 10 minutes, until the dough becomes smooth, elastic, and slightly tacky but not sticky. It should pull away from the sides of the bowl.
You can also knead by hand. Turn the shaggy dough out onto a lightly dusted work surface and knead for about 12 to 15 minutes, until it’s smooth, elastic, and slightly tacky. Be careful not to add too much extra flour, just enough to keep it from sticking to your hands and the counter.
Transfer the dough to a lightly oiled or floured bowl, cover, and let rest at room temperature until doubled in size, about 1 to 1 1/2 hours depending on your kitchen.
Turn the dough out onto a lightly floured surface and roll into a rectangle about 1/2 inch thick. Using a 4 1/2-inch round cutter, cut out circles. Use a smaller cutter to cut out the center holes.
Place each doughnut onto its own small square of parchment paper. This makes transferring them into the oil much easier later and keeps their shape intact.
Cover loosely and let rest again for 45 minutes, until noticeably puffy.
While the doughnuts rest, make the glaze. Melt the salted butter in a light-colored saucepan over medium heat, swirling often, until the milk solids on the bottom turn golden brown and smell nutty, about 5 to 7 minutes. Remove from the heat and whisk in the maple syrup. Let cool for a minute, then whisk in the powdered sugar, vanilla, and salt. Add milk or cream a little at a time until you reach the consistency you like. Keep it somewhere warm so it stays dippable.
*we’re using salted butter AND adding salt to both the dough and the glaze! I specifically use Diamond Crystal kosher salt here, which is less salty than regular table. If you’re using a different salt, cut the amount by about half so the glaze doesnt end up too salty*
Meanwhile, heat the oil to 335 to 350°F. Keep the oil within this range. Lower than 335°F and they will absorb oil. Higher than 350°F and they will brown too quickly before cooking through.
Carefully lower the doughnuts into the oil, using the parchment to guide them in. Fry for about 1 1/2 to 2 minutes per side, until deeply golden and puffed. Do not overcrowd the pot. I prefer to fry one to two at a time. Depending on the size of the pot or pan that I'm using.
Set onto a paper towel lined baking sheet, just to drain of any excess oil.
Dip into your glaze and set onto a wire rack placed inside a baking sheet. (if you'd like to make clean-up even easier, line the baking sheet with paper towels). Let set for a few minutes before serving so the excess glaze has time to drip off. If the glaze thickens while you work, whisk in a splash more milk. Best enjoyed the same day !!
