Preheat and prep the pan: Preheat the air fryer to 350°F (175°C) for 3–5 minutes. Lightly grease your baking dish with a bit of butter or nonstick spray.
Make the peach filling: In a bowl, combine peaches, granulated sugar, cornstarch, cinnamon, lemon juice, vanilla, and 2 tablespoons melted butter. Toss until the peaches are evenly coated and glossy.
Make the topping: In another bowl, whisk flour, brown sugar, baking powder, and salt. Stir in 4 tablespoons melted butter and milk just until a soft, thick batter forms. It should be scoopable, not runny.
Assemble: Spoon the peach mixture into the greased dish in an even layer. Dollop the topping over the peaches in rustic mounds, leaving some gaps so steam can escape. Sprinkle with a pinch of cinnamon or coarse sugar if you like.
Air fry: Place the dish in the air fryer basket. Cook at 350°F (175°C) for 16–22 minutes, until the topping is golden-brown and the peach filling is bubbling at the edges. Start checking at 15 minutes; every air fryer runs a little differently.
Rest: Let the cobbler sit for 5–10 minutes. This helps the juices thicken and keeps the topping crisp.
Serve: Spoon into bowls and top with vanilla ice cream, whipped cream, or a drizzle of heavy cream.