Reduce the apple cider: Pour the apple cider into a small saucepan and bring it to a gentle simmer over medium heat. Cook until it reduces to about 3/4 cup. Remove from the heat and let it cool.
Prepare the loaf pan: Preheat the oven to 350°F. Grease a 9x5-inch loaf pan and line it with parchment paper, leaving some overhang on the sides for easy removal.
Combine the dry ingredients: In a medium bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, and nutmeg until evenly combined.
Mix the wet ingredients: In a separate large bowl, whisk together the melted butter, brown sugar, and granulated sugar. Add the eggs and vanilla and whisk until smooth. Stir in the sour cream and cooled reduced apple cider.
Make the batter: Gradually add the dry ingredients to the wet ingredients. Gently fold with a spatula just until combined. Do not overmix the batter.
Fill the loaf pan: Transfer the batter to the prepared loaf pan and spread it evenly. Gently smooth the top with a spatula.
Bake and cool: Bake for about 45–50 minutes, or until a toothpick inserted into the center comes out clean or with a few moist crumbs. Let the loaf cool in the pan for about 10 minutes, then transfer it to a wire rack.
Add the cinnamon-sugar coating: Brush the warm loaf with melted butter. Mix the granulated sugar and cinnamon together, then sprinkle and gently press the mixture over the top and sides of the loaf.
Slice and serve: Allow the loaf to cool enough to slice cleanly. Cut into thick slices and serve slightly warm or at room temperature.