Preheat the oven to 350°F (177°C) and grease a 9×13-inch baking pan.

Whisk the flour, baking powder, baking soda, salt, cinnamon, nutmeg, ginger, and allspice together in a large bowl. Set aside.

Whisk the oil, granulated sugar, brown sugar, applesauce, eggs, vanilla extract, and orange juice together in a medium bowl. Pour the wet ingredients into the dry ingredients and whisk until combined. Fold in the chopped apples until combined.

Pour and spread batter evenly into the prepared pan. Bake for 45–50 minutes or until a toothpick inserted comes out clean.

Remove the cake from the oven and set the pan on a wire rack. Allow to cool for at least 30 minutes before topping or serving.

Right before serving, top the slightly warm cake with a dusting of confectioners’ sugar or make the brown sugar glaze.

Combine the butter, brown sugar, heavy cream, and pinch of salt in a medium saucepan over medium heat. Stir until the butter has melted, then let it come to a boil for 1 minute.

Turn the heat down to low, stir briefly, and let simmer for 1 minute. Remove from heat and whisk in the sifted confectioners’ sugar. Allow the glaze to cool and thicken for at least 20 minutes.

Spoon glaze over the cake right before serving.