Preheat oven to 350°F (180℃). Lightly grease a 9"x12" baking dish; set aside.
Next, cook the sliced peaches, sugars, salt, cornstarch, cinnamon, nutmeg, salt, and vanilla in a pan over medium heat. Stir often until the sugar dissolves and the peaches release their juice, 5-7 minutes. Remove from heat and set aside to cool for a few minutes.
Pour the warm peach mixture into the baking dish.
Separate cinnamon rolls, cut each slice into six pieces and arrange them in a single layer over the top of the peaches.
Cover the baking dish with aluminum foil and bake for 40-45 minutes, or until the cinnamon rolls are lightly brown and the center sets. Take the foil off about 20 minutes before the end of the baking time.
While the cobbler bakes, make the glaze. Mix the powdered sugar, vanilla, and milk in a small bowl until thoroughly combined and smooth.
Remove the cobbler from the oven and allow it to cool for about 10 minutes or until warm to the touch.
Glaze peach cobbler and serve warm with vanilla ice cream if desired. Enjoy!