Prep the oven and pan: Preheat oven to 350°F (175°C). Grease a 9x13-inch baking dish or similar casserole with butter or nonstick spray.
Peel and slice apples: Peel, core, and slice apples about 1/4-inch thick.
Keep slices uniform so they cook evenly.
Make the apple filling: In a large bowl, toss apples with brown sugar, granulated sugar, cinnamon, nutmeg, flour or cornstarch, lemon juice, vanilla, and a pinch of salt.
Start the butter base: Melt 4 tablespoons of butter and stir it into the apples. Spread the apple mixture in the prepared dish.
Par-bake the apples: Bake uncovered for 15 minutes to soften the fruit. This helps the rolls bake through without overbrowning.
Prepare the cinnamon rolls: While apples par-bake, open the cinnamon roll cans.
Cut each roll into quarters for bite-sized pieces that bake evenly.
Add the topping: Remove the dish from the oven. Arrange the cinnamon roll pieces over the hot apples in a single layer. Dot the top with the remaining 2 tablespoons of butter, cut into small cubes.
Bake until golden: Return to the oven and bake 22–28 minutes, until the rolls are puffed, golden, and cooked through in the center.
The filling should be bubbling.
Finish with icing: Let the cobbler rest 5–10 minutes. Warm the icing packets slightly and drizzle over the top. For extra shine, add a splash of milk to thin the icing if needed.
Serve: Spoon into bowls and serve warm.
Add a scoop of vanilla ice cream or whipped cream for contrast.