Prep the oven and dish: Preheat the oven to 350°F. Grease a 13 x 9-inch baking dish with nonstick cooking spray and set aside.
Separate the dough: Divide the crescent roll dough into 16 triangles, 8 from each can.
Prep the apples: Peel and core the apples, then cut each one into 8 wedges so you have 16 apple slices total.
Wrap and arrange: Roll one apple slice in each triangle of dough, starting at the wide end. Arrange them in a single layer in the prepared dish.
Make the sauce: In a large bowl, whisk together the granulated sugar, brown sugar, melted butter, vanilla extract, and cinnamon until the brown sugar has no lumps.
Pour it over the top: Spoon or pour the butter mixture evenly over the dumplings.
Add the soda: Pour the Mountain Dew in the center and around the edges of the dish, but not directly over the dumplings.
Bake: Bake for 35 to 40 minutes, until the dumplings are deep golden brown and crisp on top and the sauce bubbles at the edges.
Rest, then serve: Let the dish rest for at least 10 to 15 minutes so the sauce can thicken slightly. Serve warm with vanilla ice cream, spooning some of the pan sauce over the top.