Preheat your oven to 350°F.
In a large bowl, whisk the two large eggs, ½ cup granulated sugar, and ½ cup dark brown sugar together until pale and slightly frothy, about 2 minutes.
To the egg sugar mixture, add the 1 cup neutral oil, ½ cup applesauce, and 1 ½ teaspoon vanilla extract. Whisk together until well combined.
To the bowl add the 2 cups all purpose flour, 1 teaspoon baking powder, 1 teaspoon cinnamon, ½ teaspoon nutmeg, ¼ teaspoon cloves, ¼ teaspoon allspice, and ½ teaspoon salt. Whisk together until almost fully combined.
Add the diced apples to the batter and fold in with a spoon until just combined.
Transfer the cake batter into a prepared 8x8 baking pan.
Bake for 35-40 minutes until the edges are lightly golden brown and the center is cooked through.
Let rest in the pan for 15 minutes to set before removing and transferring to a cooling rack to cool completely. Top with powdered sugar if desired.