Preheat the oven to 350°F, and lightly grease a 2.5 quart baking dish.
In a large mixing bowl, combine the peach slices sugar, cornstarch, and cinnamon. Pour the peach mixture into the baking dish.
Cut the cinnamon rolls into fourths and place them in an even layer over the top of the peaches. Cover the baking dish with aluminum foil, and bake for 20 minutes. Remove the foil, and bake for an additional 20 to 25 minutes or until the cinnamon rolls are lightly browned and the center is set.
While the cobbler bakes, make the icing. In a small bowl, combine the powdered sugar, vanilla, and milk.
Remove the cobbler from the oven and allow it to cool until just warm before icing.