Make the crumb topping: In a medium bowl, whisk together the flour, granulated sugar, brown sugar, melted vegan butter, and cinnamon until well combined. Set aside.
Make the apple layer: In a medium bowl, toss together the chopped apples, granulated sugar, flour, and cinnamon until well combined. Set aside.
Make the cinnamon sugar layer (optional): In a small bowl, mix together the brown sugar and cinnamon. Set aside.
Make the vanilla cake: Preheat the oven to 350°F (180°C). Grease an 8-inch square baking pan and line with parchment paper, leaving some overhang on the sides.
In a large bowl, whisk together the flour, granulated sugar, baking powder, and salt.
In a separate bowl, whisk together the applesauce, oil, dairy-free milk, apple cider vinegar (if using), and vanilla extract.
Pour the wet ingredients into the dry ingredients and stir until just combined (do not overmix).
Spread the batter evenly into the prepared baking pan. Top with the apple layer, then the crumb topping, and finally the cinnamon sugar layer (if using).
Bake for 40-45 minutes, or until a toothpick inserted in the center comes out clean. Allow to cool completely before slicing and serving.
