Preheat the oven to 425 degrees. Prepare a 9x13 baking dish with nonstick cooking spray.
In a large bowl, stir together the filling for the cobbler: peaches, sugar, brown sugar, cinnamon, lemon juice, and cornstarch. Transfer the peach filling to the baking dish.
Bake uncovered for 10 minutes.
As the peaches cook, pulse together the flour, sugar, brown sugar, baking powder, and salt in a food processor. Add the butter, pulsing until the mixture resembles sand. Add the water and pulse until the dough comes together into a smooth paste.
Carefully remove the baking dish from the oven. Add dollops of the dough mixture over the peaches.
Stir together the cinnamon topping and sprinkle evenly over the dough.
Return the cobbler to the oven and bake for 25 to 30 minutes or until the topping is golden brown and the peaches are bubbling.
Serve warm with vanilla ice cream if desired.