Add 1 cup apple cider to a small saucepan and bring to a simmer over medium-low heat. As the cider is simmering, it will begin to reduce. Continue for about 5–10 minutes, or until the cider has reduced by half. (You will need ½ cup of reduced apple cider for the loaf batter. Set aside to cool slightly.)
Preheat the oven to 350°F and line a loaf pan with parchment paper, leaving some overhang on the sides for easy loaf removal.
In a bowl, sift together the dry ingredients and set aside.
2 cups all purpose flour, ½ tsp baking soda, 1 tsp baking powder, 2 tsp apple pie spice, ½ tsp salt
In a separate large bowl, whisk together the wet ingredients until combined.
3/4 cup brown sugar, 1/4 cup granulated sugar, 2 large eggs, 1 ½ tsp vanilla extract, 1/2 cup unsalted or salted butter, melted and cooled, 1/2 cup applesauce, 4 oz cup, 1/2 cup apple cider, reduced (1 cup before reducing)
Add in the dry ingredients and whisk just until combined. Do not overmix.
Pour the batter into the prepared loaf pan. Bake at 350°F for 40–45 minutes, or until a toothpick or fork inserted into the center comes out clean or with a few moist crumbs.
Allow the loaf to cool in the pan for 10–15 minutes, then use the parchment paper to lift it out and transfer it to a wire rack to cool completely.
Once the bread loaf is slightly cooled, brush the top of the loaf with melted butter and then sprinkle it with cinnamon sugar topping. (Drizzle with brown sugar icing if desired.)
1 Tbsp unsalted butter, melted, 1 1/2 Tbsp granulated sugar, 2 tsp ground cinnamon
In a small bowl, whisk together the ingredients for the brown sugar icing. Drizzle the brown sugar icing over the apple cider donut loaf. (This step is optional.)
1 cup powdered sugar, 1/2 Tbsp whole milk, ½ tsp ground cinnamon, 1/2 Tbsp brown sugar
Slice and serve warm.