Preheat the oven to 350 degrees F (175 degrees C) with a baking sheet inside.
Combine flour, ½ cup white sugar, and baking powder in a medium bowl; stir in milk and ¼ cup butter until smooth. Set batter aside.
Combine water, brown sugar, and cornstarch in a medium saucepan; stir in peaches and blueberries. Cook and stir over medium heat until thick and bubbly; stir in 1 tablespoon butter and lemon juice until butter melts. Transfer peach mixture to a 1 ½ quart ungreased baking dish.
Dollop batter in mounds over hot fruit mixture. Combine coarse sugar and nutmeg in a small bowl; sprinkle over batter.
Place the baking dish on the baking sheet and bake in the preheated oven until bubbly and a toothpick inserted into biscuit topping comes out clean, about 35 minutes.
Peach Berry Cobbler · Dinner Match Lab | Dinner Match Lab