Preheat the oven to 425°F. Spray a 9x13 deep-sided baking dish with cooking spray and set aside.
In a large bowl combine the peaches, lemon juice, sugar, brown sugar, cinnamon, allspice, vanilla extract, and cornstarch. Stir well to coat all peaches.
Pour peach mixture into the bottom of your greased 9x13 baking dish. Place in the oven to bake peaches for about 10 minutes while you make the crust and cinnamon sugar topping.
In a separate medium bowl combine flour, sugar, brown sugar, baking powder, salt, and grated butter. Stir to combine.
Pour hot water into a bowl and mix until a dough mixture forms.
In a separate small bowl combine the sugar and cinnamon, stir well.
Remove your peaches from the oven and drop spoonfuls of the crust topping mixture on top of the peaches. Use a spoon or spatula to spread out the crust topping mixture so it’s evenly covering the peaches. Sprinkle the cinnamon-sugar topping evenly over the top of the crust topping.
Place back in the oven and let cook for 25 to 30 minutes, or until the crust topping is browned and the peach juices are bubbling up on the sides of the cobbler.
Serve warm with vanilla ice cream.