Preheat your oven to 350°F. Unroll the crescent dough. Place one apple quarter at the wide end of each dough triangle and roll it up. Pro Tip: Pinch the side seams of the dough shut. This traps the apple juices inside the pastry as it bakes.
Place the dumplings in a 9x13 baking dish with the seam side down. This allows the smooth top of the pastry to brown evenly while the tucked edges soak up the sauce.
Sprinkle the cinnamon directly onto the dry dough before adding the liquid. This allows the spice to adhere to the pastry rather than just floating in the sauce.
In a saucepan, combine the butter, orange juice, and sugar. Bring to a simmer over medium heat for 2–3 minutes. You want the sugar to fully dissolve and the sauce to begin slightly thickening into a syrup before it hits the oven.
Remove from heat, stir in the vanilla, and pour the hot sauce around the dumplings rather than directly over the tops. This keeps the very top of the pastry crisp while the bottom "poaches" in the orange-caramel.
Bake for 30 minutes. The pastry should be a deep golden brown and the sauce should be bubbling.
Use a spoon to baste the dumplings with the hot pan sauce immediately after taking them out of the oven. This creates a professional, glossy shine.