Preheat the oven to 350 degrees Fahrenheit and grease a 9x13 inch baking pan.

In a medium bowl, whisk together 2 1/2 cups flour, 2 1/2 teaspoons baking powder, and 1/2 teaspoon salt.

In a large bowl, whisk 3/4 cup oil and 1 1/2 cups sugar until combined, then add 3 eggs one at a time, followed by 1/2 cup applesauce and 2 teaspoons vanilla, whisking until smooth.

Fold the dry ingredients into the wet mixture until just combined, avoiding overmixing.

Stir together 1/2 cup sugar and 3 tablespoons cinnamon in a small bowl and set aside.

Peel, core, and chop apples, then fold the 5 to 6 chopped apples into the batter.

Spread half the batter into the pan, sprinkle half the cinnamon-sugar mixture over it, top with remaining batter, and finish with the remaining cinnamon-sugar.

Bake for 50 to 55 minutes until golden brown and a toothpick comes out clean.

Let the cake cool in the pan for at least 15 minutes before slicing and serving.