Preheat your oven to 350°F (175°C). Lightly grease a 9×13-inch baking dish with butter or nonstick spray.
Open the cans and cut each cinnamon roll into quarters. Set aside the icing for later.
Spread the quartered cinnamon rolls evenly in the baking dish.
Sprinkle cinnamon and nutmeg over the cinnamon rolls.
Evenly sprinkle the dry cake mix over the cinnamon rolls. Do not mix or stir—this is key for a dump cake!
Stir 1 teaspoon vanilla extract into the melted ¾ cup butter. Pour this mixture evenly over the dry cake mix, making sure to cover as much as possible.
Bake for 15-20 minutes, or until a toothpick inserted into the center comes out clean (or with a few moist crumbs).
At this point, check the cake: If any spots of dry cake mix remain, evenly distribute small pats of the remaining ½ stick cold butter over those areas.
Continue baking for another 15-20 minutes, or until golden brown and fully cooked.
Let the cake cool for 5-10 minutes before drizzling with icing, or allow to cool longer for cleaner slices. For easier drizzling, slightly warm the icing packet by placing it in a bowl of warm water for a few minutes. Drizzle the reserved cinnamon roll icing over the top.
Scoop and enjoy!