Preheat your oven to 350°F (175°C).
Grease and line three 8-inch round cake pans with parchment paper.
In a large bowl, whisk together the flour, granulated sugar, light brown sugar, baking powder, baking soda, salt, ground cinnamon, ground ginger, ground nutmeg, and ground allspice.
In another bowl, mix the vegetable oil, plant-based milk, dairy-free yogurt, apple cider vinegar, and vanilla extract until smooth.
Add the wet ingredients to the dry ingredients, mixing until just combined.
Fold in the grated apples.
Divide the batter evenly among the prepared pans.
Bake for 25-30 minutes, or until a toothpick inserted into the center comes out clean.
Allow the cakes to cool in the pans for 10 minutes, then transfer to a wire rack to cool completely.