Preheat the oven to 350 degrees F. Butter a 9-by-13-inch pan.
Peel and core the apples, then cut each into 8 slices. Roll each apple slice in a crescent roll piece, then transfer to the prepared pan.
Melt the butter in a saucepan, then add the sugar and barely stir. Add the vanilla and stir slightly, then pour the entire mixture over the apples. Pour the citrus soda around the edges of the pan. Sprinkle with cinnamon and bake until golden brown and crispy on top, about 40 minutes.
Serve, spooning some of the sweet sauces from the pan over the top.