01 - Preheat oven to 350°F. Grease and flour a 9x5-inch loaf pan or line with parchment paper.
02 - Simmer the apple cider in a small saucepan over medium heat until reduced to 1/2 cup, about 10–15 minutes. Allow to cool slightly.
03 - Whisk the reduced apple cider, applesauce, eggs, vegetable oil, and vanilla extract in a large bowl until fully incorporated.
04 - In a separate bowl, whisk together the flour, granulated sugar, light brown sugar, baking powder, baking soda, ground cinnamon, ground nutmeg, ground allspice, and salt.
05 - Add dry ingredients to wet mixture and stir just until combined. Avoid overmixing.
06 - Pour batter into prepared loaf pan and smooth the top.
07 - Bake for 45 to 55 minutes, or until a toothpick inserted in the center emerges clean.
08 - Let loaf cool in the pan for 10 minutes, then transfer to a wire rack.
09 - While warm, brush loaf top with melted butter. Mix cinnamon and sugar for topping in a small bowl; sprinkle generously over loaf.
10 - Allow loaf to cool completely before slicing and serving.