Preheat the oven to 350°F (180°C). Spray a 9x13 baking dish with non-stick spray.
Add sliced peaches, lemon juice, white sugar, cornstarch, vanilla extract, cinnamon, nutmeg and salt to a mixing bowl and toss together. Set aside.
Add all purpose flour to a mixing bowl along with white sugar, baking powder and salt and mix together.
Add vegan butter and mix in with your hands until crumbly.
Add soy milk and mix into a thick batter.
Place the peaches into a 9x13 dish and smooth down.
Spread the batter on top and use your fingers to spread it out as best you can over the top of the peaches.
Place into the oven and bake for 55 minutes.
The topping should be golden brown and cooked through. Check carefully by inserting a toothpick into the center of the cobbler to make sure that the topping is cooked through.
Serve warm topped with a scoop of vegan ice cream or vegan whipped cream.