Preheat the oven to 325°F (160°C) and spray a 9×13 dish with non-stick spray.
Sift the flour into a bowl, then add brown sugar, baking soda, salt, cinnamon, and nutmeg. Mix together.
Make vegan buttermilk: Add 1 tbsp lemon juice to 1 cup soy milk, stir, and let it curdle for a minute.
Add the vegan buttermilk, oil, vanilla, apple cider vinegar, and applesauce to the dry ingredients. Mix well.
Fold in the chopped apple pieces.
Transfer the batter to the prepared baking dish and smooth it down.
Make the topping: Mix sugar, cinnamon, and softened vegan butter until crumbly.
Sprinkle the topping over the batter and bake for 45 minutes or until a toothpick comes out clean.
Serve warm with vegan whipped cream or ice cream.