Mix the dry ingredients. In a bowl, whisk 3 1/2 cups all-purpose flour, 1 cup sugar, 2 teaspoons baking powder, 1/2 teaspoon baking soda, 1 teaspoon kosher salt, and 1/2 to 3/4 teaspoon freshly grated nutmeg.
Cream the butter and eggs. In a separate large bowl, beat 4 tablespoons softened butter with 2 large eggs and 2 teaspoons vanilla until smooth.
It won’t get fluffy like cake batter—that’s fine.
Add the sour cream. Fold in 1 cup full-fat sour cream until fully combined. The mixture should look thick and creamy.
Bring it together. Add the dry ingredients to the wet mixture in two additions. Stir gently until no dry spots remain.
The dough will be soft and slightly sticky.
Chill. Scrape the dough onto a lightly floured sheet of parchment. Pat into a 1/2-inch-thick slab, cover, and chill for at least 1 hour (or up to overnight). Chilling helps the donuts keep their shape and fry evenly.
Heat the oil. In a heavy pot, heat 2–3 inches of oil to 350–360°F (175–182°C). Use a thermometer for accuracy.
Cut the donuts. Flour your surface and a rolling pin.
Roll the chilled dough to about 1/2 inch thick. Cut with a 3-inch donut cutter (or use a 3-inch and 1-inch round cutter). Reroll scraps once if needed.
Fry in batches. Carefully slide donuts into the hot oil, 3–4 at a time.
Fry about 1–1 1/2 minutes per side, until deep golden with a crisp edge. Keep oil between 350–360°F; adjust heat as needed.
Drain. Use a slotted spoon to transfer donuts to a wire rack set over a sheet pan. Let cool 5–10 minutes before glazing.
Make the glaze. Whisk 2 cups powdered sugar, 3–4 tablespoons milk or cream, 1 teaspoon vanilla, and a small pinch of salt until smooth and pourable. Adjust with more milk or sugar as needed.
Glaze. Dip each warm donut top into the glaze, let excess drip off, then return to the rack.
For a classic finish, dip twice, letting the first coat set slightly before the second.
Optional: Bake instead of fry. For a lighter take, pipe the dough into greased donut pans and bake at 350°F (175°C) for 12–15 minutes, until set and lightly golden. Texture will be more cakey and less crisp.