Prepare Dry Ingredients: In a medium-sized mixing bowl, whisk together the flour, baking powder, cinnamon, and salt. Set aside.
Mix Wet Ingredients: In a large mixing bowl, using electric hand beaters or a stand mixer with the paddle attachment, add both sugars, eggs, and vanilla to the bowl. Beat on medium speed for 30 seconds until well combined. Scrape down the sides.
Add Olive Oil: With the mixer running on medium, slowly drizzle in the olive oil in a steady stream, taking about 1 minute, to emulsify.
Add Applesauce: Beat in the applesauce for 15 seconds until combined.
Add Dry to Wet: Gradually add the flour mixture to the wet ingredients, beating just until no lumps or streaks of flour remain, about 25-30 seconds. Avoid over-mixing.
Fold in Apples: Fold in 1 cup of the chopped apple mixture until evenly distributed.
Transfer Batter: Pour the batter into the prepared baking tin, smoothing out the top.
Add Topping: Evenly distribute the remaining cup of apple mixture over the batter.
Bake: Bake for 50-55 minutes, or until a toothpick inserted into the center comes out clean or with a few moist crumbs, not wet batter.
Cool in Pan: Allow the cake to cool in the pan for 15 minutes. Carefully remove the cake from the pan and place it on a wire rack to cool completely.
Dust and Enjoy: Before serving, dust with powdered sugar. Enjoy!