Preheat oven to 350°F. Grease a 9- x 5-inch loaf pan and line bottom with parchment paper.

Using a mixer, cream together butter and sugar until lightened, about 3 minutes. Add eggs one at a time, waiting until the first is fully incorporated before adding the second. Increase speed to medium-high and beat for 2 minutes.

In a medium bowl, use a fork to combine flour, baking powder, baking soda, salt, cinnamon, and ginger. In a separate bowl or large measuring cup with a spout, stir together applesauce, molasses, and oil.

With the mixer on low, add one-third of the dry ingredients to the butter mixture and combine for one minute. Add half of the applesauce mixture and combine for another minute. Add another third of the flour mixture and mix to incorporate. Add the last of the applesauce mixture and combine. Lastly, scrape down the sides of the bowl and add the final third of the dry ingredients. Beat for 2 minutes until fully incorporated.

Transfer batter to prepared loaf pan and bake until a toothpick inserted into the middle comes out clean, about 1 hour and 5 minutes. Allow to cool completely before removing from pan, dusting with powered sugar if desired, and slicing.