Preheat and prep: Heat your oven to 350°F (175°C). Line a 9×5-inch loaf pan with parchment paper, leaving a bit of overhang for easy lifting later.
Reduce the apple cider: Pour ½ cup apple cider into a small saucepan. Simmer over medium heat until reduced by half (about 10 minutes). Set aside to cool — you’ll end up with ¼ cup of concentrated cider.
Cream the butter and sugar: In a large bowl (or stand mixer with paddle attachment), beat the softened butter and brown sugar for 2–3 minutes until light and fluffy. Add the vanilla and eggs; mix just until smooth.
Combine wet ingredients: In a small bowl, whisk together the applesauce, yogurt, and cooled reduced cider.
Mix the dry ingredients: In another bowl, whisk flour, baking powder, baking soda, salt, cinnamon, and nutmeg.
Bring it together: Add half the dry mixture to the butter-egg mixture, then half the wet mixture. Repeat, mixing gently between additions. Do not overmix — just fold until no flour streaks remain.
Bake: Spread the batter evenly into your prepared loaf pan. Bake for 40–50 minutes, or until a toothpick inserted in the center comes out clean. Let the loaf cool in the pan for 10 minutes.
Add the cinnamon-sugar topping: In a small bowl, mix the sugar and cinnamon. Brush the warm loaf (top and sides) with melted butter, then press or sprinkle the cinnamon sugar all over until fully coated.