Simmer 1 cup apple cider in a small saucepan until reduced to about 2 tablespoons and syrupy, 10–15 minutes. Set aside to cool.
Whisk together flour, baking powder, baking soda, cinnamon, nutmeg, and salt in a bowl.
In a separate large bowl, whisk melted butter and brown sugar until smooth. Add eggs, buttermilk, cooled cider reduction, and vanilla; mix until combined.
Fold the dry ingredients into the wet until just combined. Avoid overmixing to keep donuts tender.
For frying: heat oil to 360°F (182°C) and fry batter dollops 2–3 minutes per side until golden. For baking: fill donut pan cavities 3/4 full and bake at 350°F (175°C) for 10–12 minutes.
Mix granulated sugar and cinnamon. While donuts are warm, roll them in the cinnamon-sugar so it adheres. Cool slightly on a rack.
Notes
Use a candy thermometer for consistent frying temperature.
Baked donuts are a lighter alternative and brush with melted butter for better sugar adhesion.
Fresh apple cider gives the best flavor; store-bought juice works if reduced the same way.