Bloom the yeast: In a small bowl, combine warm milk and a pinch of the sugar. Sprinkle the yeast over the top, stir, and let it sit for 5–10 minutes until foamy. If it doesn’t foam, start over with fresh yeast.

Mix the dough: In a large bowl, whisk the remaining sugar, salt, and 3 1/4 cups flour. Add the bloomed yeast mixture, melted butter, and egg. Stir with a wooden spoon until a shaggy dough forms.

Knead until smooth: Turn the dough onto a lightly floured surface. Knead 6–8 minutes, adding small sprinkles of flour only if sticky. You’re aiming for a smooth, slightly tacky dough that holds its shape.

First rise: Place the dough in a lightly greased bowl, cover, and let it rise in a warm spot until doubled, about 1–1.5 hours.

Roll and cut: Punch down the dough and roll it to about 1/2-inch thickness. Cut doughnuts with a 3-inch cutter and use a smaller cutter for the holes. Gather scraps, rest them 5 minutes, then re-roll.

Second rise: Arrange doughnuts on parchment-lined sheets. Cover loosely and let them puff until slightly jiggly and airy, 30–45 minutes.

Heat the oil: Pour 2 inches of oil into a heavy pot. Warm to 350°F, using a thermometer for accuracy. Keep the temperature between 350–365°F throughout frying.

Fry the doughnuts: Fry 2–3 at a time, 45–60 seconds per side, until golden. Transfer to a wire rack set over a sheet pan. Fry the holes for about 30 seconds per side.

Make the glaze: Whisk powdered sugar, maple syrup, melted butter, vanilla, salt, and 2 tablespoons milk until smooth and pourable. Add a bit more milk if needed. The glaze should cling but not clump.

Dip and set: While doughnuts are warm but not scorching, dip the top of each into the glaze. Let excess drip off, then return to the rack. Add toppings while the glaze is tacky.

Serve: Let the glaze set 10–15 minutes. Enjoy warm for peak texture and flavor.