In a large bowl, add the flour, sugar, baking powder, salt, and nutmeg. Whisk everything together thoroughly so the baking powder and spices are evenly distributed.
In another bowl, whisk together the sour cream, melted butter, egg, and vanilla extract until smooth and well combined.
Pour the wet mixture into the dry ingredients and gently mix until a sticky dough forms. Do not overmix, or the donuts will turn tough.
Wrap the dough and refrigerate for at least 1 hour. This makes it easier to handle.
Roll the chilled dough on a floured surface to about ½-inch thickness. Cut into donuts and donut holes. Re-roll scraps gently.
Heat oil to 325°F (165°C). Fry 2–3 donuts at a time for about 2 minutes per side until golden brown. Remove and drain on paper towels.
Mix powdered sugar, milk, and vanilla to make glaze. Dip slightly warm donuts, let excess drip off, and allow glaze to set.