Preheat the oven to 350°F.
Cut the vegan butter into 6 to 8 slices. Place them into a small dish, then place the dish into the freezer. Leave it there while you proceed with the next steps.
Whisk the flour, sugar, baking powder, and salt together in a large mixing bowl.
Stir ⅔ cup of chilled non-dairy milk together with the apple cider vinegar in a small bowl or container, such as a liquid measuring cup.
Remove the butter from the freezer and add it to the bowl with the flour mixture. Use a pastry cutter or fork to cut the butter into the flour mixture. Continue until the mixture resembles coarse crumbs, and work quickly to avoid warming up the butter too much.
Add the milk mixture to the bowl with the flour mixture. Stir just until the ingredients are combined and a dough forms. Place the bowl into the fridge to chill while you make the filling.
Chop any large berries, such as strawberries, into smaller pieces (quarter large ones, or halve small ones). You'll also want to hull any strawberries, and pit any cherries if you're using them.
Place the berries into a large mixing bowl. Add the sugar, cornstarch, lemon zest, vanilla extract, and cinnamon, if using. Stir until the ingredients are well mixed.
Transfer the berry filling to a 2 ½ quart or slightly larger baking dish (Note 4), spreading it out evenly. Remove the topping from the fridge, and drop it in dollops over the filling. You probably won't cover all of the filling, and this is fine. Brush the topping with a tablespoon or two of non-dairy milk, then optionally sprinkle it with coarse sugar.
Bake the cobbler until the filling is bubbly throughout and the biscuits are fluffy and fully set, about 40 to 45 minutes.
Place the dish on a cooling rack when it comes out of the oven. Let it cool until it's just warm before serving, or you can let it cool completely and reheat it later.