Toss together the filling ingredients then transfer to the baking dish. Bake for 10 minutes while making the batter.
In a large bowl, combine flour, sugars, baking powder, and salt. Cut in butter with either a fork or a pastry blender until a coarse meal is formed. Pour in water and stir until just combined.
With the peaches out of the oven, drop in spoonfuls of the batter. Bake until topping is golden brown and delicious, about 25 to 30 minutes.