Warm the milk. Heat 3/4 cup whole milk until warm to the touch, about 100–110°F.
It should feel cozy, not hot. If it’s too hot, let it cool a minute to avoid harming the yeast.
Activate the yeast (if using active dry). In a small bowl, combine warm milk, 1 tablespoon granulated sugar, and 2 1/4 teaspoons active dry yeast. Stir and let stand 5–10 minutes until foamy.
If using instant yeast, skip this step and add it directly to the flour in the next step.
Make the dough. In a large bowl, mix 3 cups all-purpose flour, 1/4 cup granulated sugar, 1/2 teaspoon salt, and a pinch of ground nutmeg. Add 2 beaten eggs, the milk-yeast mixture (or warm milk if using instant yeast), and 4 tablespoons melted, cooled butter. Stir until a shaggy dough forms.
Knead until smooth. Knead by hand on a lightly floured surface or with a dough hook for 6–8 minutes, adding flour only as needed to prevent sticking.
The dough should be soft, slightly tacky, and elastic. If it’s very sticky after 2 minutes, sprinkle in an extra tablespoon or two of flour.
First rise. Place the dough in a lightly greased bowl, cover, and let rise in a warm spot until doubled, about 60–90 minutes. A slow, steady rise builds better flavor than rushing it.
Shape the doughnuts. Turn the dough onto a floured surface and roll to about 1/2-inch thick.
Cut rounds with a 3-inch cutter and a 1-inch cutter for holes. Gather scraps, rest 5 minutes to relax the gluten, then reroll once.
Second rise. Place the cut doughnuts on parchment-lined baking sheets, lightly cover, and proof until puffy, 30–45 minutes. They should look airy and slightly jiggly when nudged.
Heat the oil. In a heavy pot, heat 2–3 inches of oil to 350°F.
Use a thermometer for accuracy. Keep a wire rack set over a baking sheet nearby.
Fry in batches. Carefully lower 2–3 doughnuts into the oil. Fry 60–75 seconds per side, turning once, until golden.
Doughnut holes take about 45 seconds per side. Adjust heat to maintain 350°F.
Drain and cool. Transfer fried doughnuts to the rack. Let cool 5–10 minutes before glazing; they should still be warm but not hot.
Make the maple glaze. In a bowl, whisk 1/2 cup pure maple syrup, 1 1/2 cups powdered sugar, 2 tablespoons melted butter, 1 teaspoon vanilla, and a pinch of salt until smooth and thick but pourable.
If needed, thin with 1–2 teaspoons warm milk or thicken with a bit more powdered sugar.
Glaze and finish. Dip the top of each warm doughnut into the glaze, let excess drip, then set back on the rack. While the glaze is still tacky, sprinkle a few flakes of sea salt on each. Go light—too much can overwhelm the sweetness.
Let set and serve. Allow the glaze to set for 10–15 minutes.
Enjoy slightly warm for peak texture and aroma.