Preheat the oven to 350°F (175°C). Grease and flour a 9-inch round cake pan.

In a mixing bowl, whisk together the dry ingredients: flour, sugar, baking powder, baking soda, cinnamon, nutmeg, and salt.

In another bowl, mix the wet ingredients: applesauce, vegetable oil, eggs, and vanilla extract until well combined.

Gradually add the wet mixture to the dry ingredients, stirring until just combined.

Fold in the chopped apples gently.

Pour the batter into the prepared cake pan.

Bake for 40-45 minutes, or until a toothpick inserted into the center comes out clean.

Allow the cake to cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.