Start by pouring 1½ cups of apple cider into a small saucepan. Simmer over medium heat for 10–15 minutes until it reduces to about ¾ cup. Let it cool slightly before adding it to the batter. This step concentrates the apple flavor and makes a big difference in taste.
In a large bowl, use a hand or stand mixer to beat the softened butter and brown sugar until light and fluffy, about 2–3 minutes. This adds air to the batter and helps the loaf rise evenly.
Beat in the eggs, one at a time, then mix in the yogurt and vanilla extract. Pour in the reduced cider and mix until smooth. It’s okay if the mixture looks slightly curdled, it’ll come together when you add the dry ingredients.
In a separate bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, nutmeg, and allspice. Slowly add this dry mixture to the wet mixture, stirring gently just until no flour streaks remain. Don’t overmix or your loaf may become dense.
Pour the batter into a greased 9×5 inch loaf pan. Smooth the top with a spatula and tap the pan lightly on the counter to release any air bubbles. Bake at 350°F (175°C) for 50–55 minutes, or until a toothpick inserted in the center comes out clean.
Let the loaf cool for 10 minutes, then carefully remove it from the pan and place it on a cooling rack. While still slightly warm, brush the top and sides with melted butter. Immediately sprinkle (or roll) the loaf in cinnamon sugar for that signature doughnut finish.