Heat oven to 350 degrees. Butter and flour an 8 1/2-inch-by-4 1/2-inch loaf pan.

In a medium bowl, whisk together flour, baking powder, cinnamon, salt, nutmeg and cloves.

In a large bowl, whisk together the oil, applesauce, sugars, eggs and apple.

Fold the dry ingredients into the wet ingredients until just combined. Transfer to the prepared pan and bake until a toothpick inserted into the center comes out clean, 50 to 60 minutes.

Add the butter, confectioners’ sugar, and salt.

Reduce the heat to maintain a simmer and continue to cook the mixture, whisking often, until it has become syrupy and thickened slightly, about 4 minutes. Set aside to cool until it thickens slightly.

Transfer to a rack to cool slightly, then remove the cake from the pan and let it cool completely.

When the cake has cooled, prepare the glaze: Bring the apple cider to a boil in a small saucepan over medium-high heat. Continue to cook the cider until it has reduced to 1/3 cup, about 10 minutes.

Drizzle the glaze over the cake, and serve.