Prepare apples: Wash, peel, and core 2 apples. Cut each apple into 8 even wedges for a total of 16 slices.
Preheat oven to 350°F. Lightly grease a 9x13-inch baking dish.
Assemble dumplings: Unroll 2 tubes crescent dough and separate into 16 triangles along perforations. Place one apple slice at the wide end of each triangle. Roll dough around apple, starting from the wide end and rolling to the point. Place seam-side down in prepared baking dish. Repeat with remaining dough and apples.
Make sauce: In a medium saucepan over low heat, melt 1 cup butter until bubbly. Stir in 1 cup brown sugar, 1 teaspoon vanilla extract, 1 teaspoon cinnamon, and ½ teaspoon nutmeg. Mix until combined (mixture may appear slightly grainy). Pour sauce evenly over dumplings in the baking dish.
Add soda: Pour 12 ounces lemon-lime soda evenly over the top of all dumplings.
Bake: Place in preheated oven and bake for 35-40 minutes, until dumplings are golden brown and sauce has thickened slightly.
Serve: Remove from oven and let cool for 5 minutes. Serve warm with sauce spooned over the top. Add vanilla ice cream if desired.
Notes
Apple varieties: Granny Smith works best, but Honeycrisp, Golden Delicious, or Braeburn are good alternatives.
Soda options: Use any citrus or lemon-lime soda. Ginger ale also works. Avoid diet sodas as they alter the sauce texture.
Make-ahead: Assemble dumplings up to 2 hours ahead, cover with plastic wrap, and refrigerate. Add sauce and soda just before baking.
Crescent roll types: Both classic and "big & buttery" Pillsbury crescents work perfectly.