Heat oven to 350°F. Lightly grease a 12-cavity donut pan.
Whisk flour, granulated sugar, baking powder, baking soda, salt, and nutmeg in a large bowl.
Stir buttermilk, melted butter, oil, and vanilla together in a separate bowl.
Pour wet ingredients into dry. Mix until just combined; do not overmix.
Pipe or spoon batter into the pan, filling each well about two-thirds full.
Bake 10–12 minutes, until tops spring back and edges are lightly golden.
Cool in the pan 5 minutes. Turn out onto a rack until just warm.
Brush donuts lightly with melted butter. Toss in powdered sugar to coat all sides.
Repeat the coating for a thicker sugar layer, if you like. Serve immediately.