While your grill heats up, make the cobbler topping by whisking together the flour, brown sugar, and baking powder in a medium bowl. In a separate small bowl, mix the melted butter with the heavy cream until combined. Pour the wet mixture into the dry ingredients and stir gently until a thick, biscuit-like dough forms—don't overmix or your cobbler topping will be tough. Set this dough aside; it should be thick and slightly lumpy, which is exactly what you want for a rustic cobbler texture.
Heat your grill to 400°F. Once hot, place the peach wedges directly on the grates and grill for about 5 minutes, flipping halfway through, until they develop light char marks and become slightly softened. Transfer the grilled peaches to a cutting board and slice them into bite-sized pieces. I find that grilling the peaches first adds a subtle smokiness that elevates the whole dish—it's a small step that makes a big difference.
In a large bowl, combine the sliced peaches from Step 2 with the brown sugar, flour, cinnamon, nutmeg, salt, lemon juice, and vanilla extract. Toss everything together until the peaches are evenly coated and the spices are well distributed. Let the mixture sit for a minute to allow the flavors to begin melding together.
Pour the seasoned peach mixture into a 10-inch cast iron skillet or similar grill-safe baking dish. Dot the top with the butter cubes, distributing them evenly across the surface—these will melt and create pockets of richness throughout the cobbler. Cover the skillet tightly with foil and place it on the cooler side of the grill (or on the grates away from direct flame). Grill covered for about 15 minutes until the peaches release their juices and begin to bubble around the edges.
Carefully remove the foil from the skillet and drop spoonfuls of the cobbler dough from Step 1 over the hot peaches, leaving some gaps so steam can escape and the fruit stays visible. Return the skillet to the grill without foil and grill for 12-15 minutes until the dough topping is golden brown and cooked through. I like to rotate the skillet halfway through cooking for even browning, especially if your grill has hot spots. The dough should look baked and set, not doughy or wet.
Remove the skillet from the grill and let the cobbler rest for about 10 minutes before serving. This resting time allows the filling to set slightly and makes serving much easier. Spoon the cobbler into bowls and top with vanilla ice cream, which will melt into the warm peaches and dough for an irresistible finish.