Preheat the oven to 350°F. Grease a 10-inch cast iron skillet or another 2-quart baking dish (such as an 11 x 7-inch pan) with nonstick cooking spray. Arrange the sliced peaches in the prepared dish.
In a large bowl, whisk together the Bisquick, sugar, milk, melted butter, cinnamon, and nutmeg until combined.
Pour the batter over the peaches.
Bake, uncovered, for about 1 hour (or until golden brown and set). The cobbler is done when the topping is totally set (like a cake), it isn't jiggly in the middle, and you can’t see any batter bubbling. If the top of the cobbler starts to get too dark, cover loosely with foil until it's cooked through.
Serve the cobbler warm with a scoop of vanilla ice cream on top!