Preheat oven to 350°F (175°C). Grease and line a 9×5-inch loaf pan with parchment paper.
In a small saucepan, simmer the apple cider over medium heat until reduced to ½ cup. Let cool.
In a medium bowl, whisk together flour, baking powder, baking soda, cinnamon, nutmeg, allspice, and salt.
In a separate large bowl, whisk melted butter, brown sugar, and granulated sugar until smooth. Add eggs, sour cream, vanilla, and cooled cider.
Gradually fold dry ingredients into wet ingredients until just combined.
Pour batter into prepared loaf pan. Bake for 45–55 minutes or until a toothpick inserted in the center comes out clean.
Let loaf cool in the pan for 10 minutes, then transfer to a wire rack.
Brush top of warm loaf with melted butter and sprinkle with cinnamon sugar mixture evenly. Let cool before slicing.