Preheat the oven to 350 degrees F and lightly grease a 2 quart baking dish. A 8x8 dish will work as well. You can even use a 9x13 dish but the cobbler will be more spread out.
Prepare the peaches: Slice or dice your peaches (peel if desired, see Note on how to best do this). Place them in the casserole dish, then sprinkle the 1/4 cup of sugar and cornstarch on top. Mix right in the dish to combine, then spread the peaches out evenly in the dish.
Make the batter: In a large bowl, mix together the melted vegan butter, sugar, vanilla and soy milk. Now add the flour, baking powder and salt and mix to combine. The batter will be thick, with a cookie dough consistency.
Using a spatula or your hands, sprinkle the batter on top of the peaches and spread out a little bit. It doesn't have to be perfect, or cover all of the peaches.
Bake for 30-35 minutes, until the crust is slightly golden and the peaches are bubbling. Remove from the oven and serve warm with a scoop of vegan vanilla ice cream or coconut whipped cream. Enjoy!