Preheat oven to 350F. Prepare two 6" cake pans by greasing each lightly with olive oil and lining the bottoms with parchment paper.
In a mixing bowl, whisk together the flour, baking powder, salt, ground cinnamon, and ground anise.
In a separate mixing bowl, beat together the olive oil, brown sugar, granulated cane sugar, eggs, and vanilla extract for 3 minutes on high speed.
Gradually mix in the flour mixture, then fold in the apple mix. Evenly pour the batter into the prepared cake pans.
Bake for 35-40 minutes, or until a toothpick comes out clean.
Allow the cakes to cool for 10 minutes in the pan, then cool completely on a wire rack before frosting/layering.