Prepare oven: Preheat oven to 375°F.
Mix batter: Combine flour, 1 cup sugar, baking powder, and salt in a medium bowl; add milk, stirring just until dry ingredients are moistened.
Pour batter into melted butter: Pour melted butter in a 13- x 9-inch baking dish. Pour batter over butter (do not stir).
Cook peaches: Bring remaining 1 cup sugar, peach slices, and lemon juice to a boil over high heat in a saucepan, stirring constantly.
Combine peach filling with batter: Pour peach mixture over batter (do not stir). Sprinkle with cinnamon, if desired.
Bake peach cobbler: Bake at 375°F for 40 to 45 minutes or until golden brown. Serve cobbler warm or cool.
