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Preheat oven to 350 F and spray donut pans with cooking spray.
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In a large bowl, whisk flour, baking powder, baking soda, and nutmeg together. Set aside.
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In a small bowl, combine egg, brown sugar, milk, and sour cream. Mix until smooth. Stir in melted butter and vanilla.
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Combine the egg mixture and the flour mixture. Do not overmix.
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Transfer the batter to a piping bag or gallon size bag with a corner cut off. Pipe batter into the greased donut pans, filling each about ⅔ of the way full.
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Bake for 10-12 minutes or until a toothpick inserted comes out clean.
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Cool in the pan for 5 minutes before transferring to a wire rack to cool completely. While donuts are cooling, make the glaze.