Pour apple cider into a saucepan and simmer until reduced by half, about 20–30 minutes. Let cool.
Preheat oven to 350°F (175°C). Grease a 9×5-inch loaf pan.
In a mixing bowl, beat softened butter and brown sugar until fluffy.
Mix in the egg and vanilla extract.
Add reduced cider, flour, apple pie spice, baking powder, baking soda, and salt. Stir gently until just combined.
Pour batter into prepared loaf pan and bake 50–55 minutes, or until a toothpick comes out clean.
Cool loaf in pan for 15 minutes, then move to a rack.
Brush with melted butter and sprinkle generously with cinnamon sugar.
Let cool for 1 hour before slicing.
