Melt butter in a 13 x 9 inch baking dish.
Combine flour, 1 cup sugar, baking powder, and salt; add milk, stirring just until dry ingredients are moistened. Pour batter over butter (do not stir).
Bring remaining 1 cup sugar, peach slices, and lemon juice to a boil over high heat, stirring constantly; pour over batter (do not stir). Sprinkle with cinnamon, if desired.
Bake at 375℉ for 40 to 45 minutes or until golden brown. Serve cobbler warm or cool.