Preheat the oven to 375° Fahrenheit.
Once oven is preheated, melt butter in a 9- x 9-inch baking dish.
While butter is melting, bring ¼ cup sugar, peach slices, and lemon juice to a boil over high heat, stirring constantly until softened and juice is extracted from peaches (about 5 minutes). Set to the side.
Using a stand mixer, combine flour, ¾ cup sugar, baking powder, and salt. Then, add milk, stirring just until dry ingredients are moistened. Pour batter over hot butter pan (do not stir). Then pour peach mixture over batter (do not stir).
Bake at 375° Fahrenheit for 30 minutes or until golden brown. Serve cobbler warm or cool.