Mix dry ingredients: In a large bowl, whisk flour, sugar, baking powder, baking soda, salt, and nutmeg.
Add wet ingredients: In another bowl, beat the egg, then mix in melted butter and buttermilk.
Combine and form dough: Add wet mixture to dry ingredients. Stir until a soft dough forms.
Roll and cut: On a floured surface, roll out dough to 1/2 inch thick. Cut out donut shapes using a cutter or two round glasses.
Heat oil: In a deep pot, heat oil to 350°F (175°C).
Fry donuts: Fry 2–3 at a time, about 1–2 minutes per side, until golden brown.
Drain and cool: Remove with slotted spoon and drain on paper towels.
Serve: Enjoy plain or dust with powdered sugar.