How to Make It
Preheat oven to 375°. Lightly grease a 9-x13-inch baking dish; set aside.
Combine the peach slices, 2 heaping tablespoons of the warm caramel sauce, brown sugar, and lemon juice or vinegar in a large mixing bowl; stir gently to combine. Pour the peaches into prepared baking dish.
Whisk together the flour, granulated sugar, baking powder, and salt in a large mixing bowl. Sprinkle butter over the flour mixture; cut the butter into the flour mixture using your fingertips. Combine the milk and vanilla in a glass measuring cup. Stir the milk mixture into the flour mixture until just combined. Pour the batter over the peaches in.
Bake for 40-45 minutes, rotating halfway through, until the crust is golden-brown and filling is bubbling. Allow to cool slightly before serving, about 1 hour. Pour remaining caramel sauce (gently re-heated if necessary) over top of the cobbler and sprinkle with flakey salt before serving.
You can make the Salted Caramel Sauce days ahead of time; simply store it in a container with a tight-fitting lid in the refrigerator. However, you will want to warm it up to use in this recipe. The caramel can be gently warmed in a saucepan over low heat (stir frequently) or in the microwave.