Heat the oven to 350Β°F. Put the butter in a 9x13-inch baking dish and place it in the oven to melt while the oven preheats, 5β8 minutes. Remove the dish once the butter is melted so it doesnβt brown.
Peel the peaches: Bring a pot of water to a boil. Score a small X on the blossom end of each peach, blanch 30β45 seconds, then transfer to an ice bath. Slip off the skins, pit, and slice into 0.5-inch wedges (about 6 cups).
In a medium saucepan, combine the sliced peaches with 0.5 cup granulated sugar, lemon juice, cornstarch, cinnamon, and nutmeg. Cook over medium heat, stirring, until the sugar dissolves and the juices just begin to simmer, 3β5 minutes. Remove from heat.
In a mixing bowl, whisk the flour, 1 cup granulated sugar, baking powder, and salt. Whisk in the milk until smooth; do not overmix.
Pour the batter evenly into the hot, buttered baking dish without stirring it into the butter. Spoon the warm peaches and their juices evenly over the batter; do not stir. The batter will rise up around the fruit as it bakes.
Bake until the cobbler is deeply golden, the edges are crisp, and the center is set, 40β45 minutes. Let cool 10β15 minutes to allow the juices to thicken slightly.
Serve warm, scooped into bowls with vanilla ice cream, if desired.