Heat oven to 400 F degrees. Lightly grease a 2-quart casserole. Peel and slice fresh peaches. Place in greased casserole. Stir in lemon juice. In 1-quart saucepan, stir together brown sugar and cornstarch. Gradually add water, stirring until cornstarch is dissolved.
Cook over medium heat, stirring constantly, until sauce thickens, 5 minutes. Pour sauce over peaches in casserole. Set aside 1 teaspoon sugar.
To prepare topping, in medium size bowl, stir together remaining sugar, flour, baking powder and salt. With wooden spoon, stir in butter and egg until a soft dough forms. Drop spoonfuls onto peach mixture (topping will spread as it bakes). Sprinkle with reserved 1 teaspoon sugar.
Bake cobbler 40-45 minutes or until topping is golden brown and filling bubbles. Cool slightly on wire rack. Sprinkle with additional sugar if desired. Serve peach cobbler warm or at room temperature.