Prepare the Peaches: If using fresh peaches, wash, pit, and slice them into bite-sized pieces. If using canned peaches, drain them thoroughly. Place the peaches in a mixing bowl. Add the brown sugar, granulated sugar, cornstarch, cinnamon, vanilla extract, lemon juice, melted butter, and salt. Gently toss everything together until the peaches are evenly coated.
Prepare the Peach Filling: Stir the peach mixture gently until the sugar and cornstarch are evenly distributed. Let it sit for a few minutes so the peaches can release some of their natural juices and the flavors can mingle.
Transfer to an Air Fryer-Safe Dish: Lightly grease an air fryer-safe baking dish that fits comfortably inside your air fryer basket. Pour the peach mixture into the dish and spread it into an even layer. Make sure there is enough space around the dish for proper air circulation.
Add the Cinnamon Rolls: Open the refrigerated cinnamon roll package and separate the rolls. Cut each cinnamon roll into smaller pieces. Arrange the pieces evenly over the peaches, leaving small spaces between them so the hot air can circulate and the cinnamon rolls cook evenly.
Air Fry the Cobbler: Preheat the air fryer to 350°F according to your model's instructions. Place the baking dish inside the air fryer and cook for about 18–22 minutes, or until the peach filling is bubbling and the cinnamon roll pieces are puffed and golden brown. Because air fryers vary, start checking the cobbler toward the end of the cooking time.
Check for Doneness: Carefully insert a toothpick into one of the thicker cinnamon roll pieces. It should come out without any raw dough attached. The peach filling should be hot, bubbling, and slightly thickened around the edges. If the cinnamon rolls are browning too quickly, loosely cover the dish with foil and continue cooking until the center is fully cooked.
Add the Icing: Carefully remove the hot baking dish from the air fryer and let the cobbler rest for about 5 minutes. Drizzle the icing that comes with the cinnamon rolls over the warm cinnamon roll topping, allowing it to melt slightly into the golden surface.
Serve Warm: Spoon the warm peach cobbler into individual serving bowls. Add a scoop of vanilla ice cream and sprinkle with chopped pecans if desired. Serve immediately while the peaches are warm, juicy, and syrupy and the cinnamon roll topping is soft and golden.