Preheat the oven to 350°F (175°C) and grease a donut pan.
In a mixing bowl, whisk together flour, sugar, baking powder, baking soda, salt, and nutmeg.
In a separate bowl, mix the buttermilk, egg, melted butter, and vanilla extract until combined.
Combine the wet and dry ingredients, mixing until just combined (no overmixing!).
Spoon or pipe the batter into the donut mold, filling each opening about 2/3 full.
Bake for 10-12 minutes until lightly golden and a toothpick comes out clean.
Allow the donuts to cool in the pan for a few minutes before transferring them to a wire rack.
Prepare the glaze by mixing powdered sugar with milk and vanilla until smooth, then drizzle over the cooled donuts.