Heat the oven to 350°F (175°C). Butter the dish and place it on a rimmed baking sheet before preparing the filling.
Toss peaches with fruit sugar, cornstarch, lemon juice, and vanilla. Spread into the dish, distributing the fruit and its juices evenly.
Whisk topping flour, sugar, baking powder, and salt. Cut cold butter into the mixture until the pieces are no larger than peas.
Pour in milk and stir just until a soft spoonable dough forms. Leave small lumps rather than beating the topping into a smooth batter.
Drop eight mounds of dough over the peaches, leaving gaps between them. The openings help the fruit steam and show when juices are bubbling.
Bake 40–50 minutes until topping is golden and cooked through. A tester in a central mound should show no wet dough.
If the top colors early, tent with foil and keep baking until central fruit juices bubble and the topping underneath has set.
Cool for 20 minutes before serving with a broad spoon. Include both peaches and topping in every portion, keeping unused cobbler covered after cooling.
