Preheat the oven to 350°F.
To make the topping, first cut the butter into 6 to 8 slices. Place them on a small dish or in a small bowl, then place it in the freezer. Let it chill while you mix the dry and wet ingredients.
Whisk the flour, sugar, baking powder, and salt together in a large mixing bowl.
Stir the milk and apple cider vinegar together in a small bowl or container.
Take the butter out of the freezer and add it to the bowl with the flour mixture. Use a pastry cutter or fork to cut the butter into the dry ingredients. Continue until the mixture looks like coarse crumbs.
Add the milk mixture and stir just until the ingredients are combined and form a very soft and sticky dough. Place the bowl in the fridge and let it chill for 10 to 15 minutes while you make the filling.
Stir all of the filling ingredients together in a large mixing bowl.
Transfer the filling to a medium (approximately 2-quart) baking dish, spreading it out evenly. Take the topping out of the fridge and arrange dollops of it on top of the filling. Try to get it relatively evenly distributed, but it's okay if there are some uncovered spots. Brush the topping lightly with a tablespoon or two of non-dairy milk.
Place the cobbler into the oven with something underneath it (such as a baking sheet) to catch any drips. Bake the cobbler until the filling is bubbly and the topping is fluffy and lightly browned on top, about 45 to 50 minutes.
Place the dish on a cooling rack when it comes out of the oven. Let the cobbler cool down until it's just warm (or let it cool completely and reheat).
Scoop into bowls and serve warm.