Make the dry mix: In a large bowl, whisk flour, granulated sugar, baking powder, baking soda, salt, and nutmeg until well combined.

Whisk the wet ingredients: In a separate bowl, whisk buttermilk, eggs, melted butter, and vanilla until smooth.

Combine gently: Pour wet into dry and stir with a spatula just until no dry streaks remain. The dough should be soft and slightly sticky. Do not overmix.

Choose your method: For frying, line a sheet pan with parchment and dust with flour. For baking, preheat the oven to 350°F (175°C) and lightly grease a donut pan.

Shape for frying: Lightly flour your hands and the dough surface. Pat the dough to 1/2-inch thickness. Cut with a floured donut cutter or use a 3-inch round cutter and a 1-inch cutter for the centers. Transfer to the prepared pan and rest 10 minutes.

Fry the donuts: In a heavy pot, heat 2 inches of oil to 350°F (175°C). Fry donuts 45–60 seconds per side until golden. Fry holes about 30 seconds per side. Keep the oil between 340–360°F for even cooking.

Drain and cool slightly: Move donuts to a wire rack set over paper towels. Let sit 3–4 minutes—warm but not hot—before coating.

Coat in powdered sugar: Add powdered sugar to a large paper bag or shallow bowl. Toss warm donuts to coat generously. Tap off excess and repeat once more for a thicker finish if you like.

For baking instead: Spoon or pipe the batter into the greased donut pan, filling each well about 3/4 full. Bake 9–11 minutes, or until they spring back when touched and a toothpick comes out clean. Cool 2 minutes, then toss in powdered sugar while still slightly warm.