Preheat the oven to 350°F. Butter a 13-by-9-inch baking dish.

Peel and core the apples. Cut each apple in half vertically, then each half into 4 wedges.

Unroll the crescent dough sheets on a lightly floured surface and separate the perforated dough into 16 triangles. Place one apple wedge on the wide base of a triangle and roll the apple toward the pointed end of the triangle. Continue with the remaining apples and crescent rolls. Place in the prepared baking dish.

In a small saucepan, melt the butter. Add the sugar and barely stir to create a lumpy, grainy mixture. Add the vanilla and barely stir again. Pour the mixture over the wrapped apples. Pour the Mountain Dew soda around the edges of the pan and sprinkle with cinnamon. Bake until the dumplings are golden brown and crispy on top, about 30 to 45 minutes.

Serve with ice cream, and spoon some of the sauce from the pan over the top.