Heat oven to 350 degrees F.
Combine peaches, 1 cup of the sugar and the water in a saucepan and mix well. Bring to a boil and simmer for 10 minutes. Remove from the heat.
Place butter in deep 2- to 3-quart baking dish. In a bowl, whisk together remaining 1 cup sugar, flour and milk slowly to prevent clumping. Pour mixture over melted butter. Do not stir. Spoon fruit on top, gently pouring in liquid. (Batter will rise to top during baking.)
Bake at 350 degrees F for 30 to 35 minutes. Remove and let cool slightly on wire rack, about 10 or 15 minutes.
To serve, scoop onto a plate and serve with vanilla ice cream, if desired. Makes 12 servings.