Preheat oven to 375°F (190°C). Grease a 9x13-inch baking dish.
In a large bowl, combine sliced peaches, sugar, lemon juice, cornstarch (or flour), cinnamon, and nutmeg. Gently toss to coat.
Pour peach mixture into the prepared dish. Dot with butter.
In a medium bowl, whisk flour, sugar, baking powder, and salt.
Cut cold butter into dry ingredients using a pastry blender or forks until mixture resembles coarse crumbs.
Stir in milk or buttermilk just until combined; do not overmix.
Drop spoonfuls of the topping over the peach mixture.
Sprinkle coarse sugar on top if desired.
Bake for 40–50 minutes until topping is golden and peaches are bubbly.
Let rest for 15–30 minutes before serving.