Prep: Preheat your oven to 350°F. Generously grease a 9x13 inch baking dish.
Assemble: Unroll the crescent triangles. Place a small spoonful of apple pie filling at the wide end of each triangle. Roll the dough toward the point, tucking the edges as needed.
Arrange: Place the dumplings in the prepared baking dish.
Glaze: In a small bowl, stir together the softened butter and brown sugar until a paste forms. Dollop a small spoonful of this mixture onto the top of each dumpling.
The "Soda Secret": Carefully pour the lemon-lime soda into the bottom of the dish around the dumplings. Tip: Do not pour it directly over the tops, or you'll wash off the sugar-butter mixture!
Bake: Bake for 35–45 minutes until the tops are deep golden brown and the dough is cooked through.
Serve: Let them cool for at least 10 minutes. The liquid in the pan will thicken into a delicious apple-caramel sauce as it sits.