**Preheat the oven**: Preheat your oven to 375°F (190°C). Lightly grease a 9x13-inch baking dish or use a seasoned cast-iron skillet.
**Prepare the peaches**: In a large bowl, toss the peach slices with 1/2 cup of the sugar, lemon juice (if using), cornstarch (if peaches are extra juicy), cinnamon, and nutmeg. Taste and add more sugar if your peaches aren’t very sweet. Spread the peach mixture evenly in the prepared dish.
**Make the batter**: In a separate bowl, whisk together the flour, baking powder, salt, and remaining 1/4 cup sugar. Stir in the milk until just combined, then pour in the melted butter and whisk gently to create a smooth batter.
**Assemble**: Pour the batter evenly over the peaches. Some peaches may peek through—that’s okay.
**Bake**: Place the cobbler in the preheated oven and bake for 35–45 minutes, or until the topping is golden brown and the peaches are bubbling around the edges.
**Cool and serve**: Let the cobbler rest for at least 10–15 minutes. Serve warm, ideally with a scoop of vanilla ice cream.