Combine flour, 3/4 cup sugar, baking powder, and salt; add milk, stirring just until dry ingredients are moistened. Pour batter over butter (do not stir).
Bring remaining 3/4 cup sugar and peach slices to a boil over high heat, stirring constantly; pour over batter (do not stir). Sprinkle with cinnamon.
Bake at 375°F for 40 to 45 minutes or until golden brown.
Serve cobbler warm with vanilla ice cream or yogurt.