Prep your equipment. If baking, heat the oven to 350°F (175°C) and lightly grease a donut pan.
If frying, set up a heavy pot with 2 inches of oil and a thermometer. Line a sheet pan with paper towels for draining.
Mix the dry ingredients. In a medium bowl, whisk together 2 1/4 cups flour, 3/4 cup sugar, 2 1/2 teaspoons baking powder, 1/2 teaspoon kosher salt, and 1/2 teaspoon ground nutmeg. This keeps the crumb light and even.
Combine the wet ingredients. In another bowl, whisk 2 large eggs, 1 cup whole milk (or buttermilk), 1 teaspoon vanilla, and 6 tablespoons melted unsalted butter (cooled so it doesn’t scramble the eggs).
Bring them together gently. Pour the wet mixture into the dry and stir with a spatula until just combined.
The batter should be thick but scoopable. Do not overmix or the donuts will turn tough.
For baked donuts: Spoon or pipe the batter into the prepared pan, filling each well about 3/4 full. Bake 10–12 minutes until the tops spring back and a toothpick comes out clean. Cool in the pan for 2 minutes, then transfer to a rack.
For fried donuts: Chill the batter 20–30 minutes so it’s easier to handle.
On a lightly floured surface, pat it 1/2-inch thick. Cut with a floured donut cutter. Heat oil to 350°F (175°C).
Fry 1–2 minutes per side until golden. Keep the oil between 340–355°F for best texture. Drain on paper towels.
Make a simple glaze (optional). Whisk 1 cup powdered sugar with 1–2 tablespoons milk and a splash of vanilla until smooth. Dip warm donuts, then let the glaze set on a rack.
Or go with cinnamon sugar. Mix 1/2 cup sugar with 1–2 teaspoons cinnamon.
Toss warm donuts in the mixture so it clings nicely.
Serve warm. These taste best within a few hours, but they keep well with a few tricks below.