Make Cinnamon Syrup: In a small saucepan, melt the butter over medium heat. Stir in the sugar and cinnamon. Heat the mixture, whisking constantly to combine. The mixture will slowly combine and begin to thicken. Once thickened, remove from the heat and stir in the vanilla extract.
Pour Over Dumplings: Pour the cinnamon mixture evenly over all the apple dumplings in the baking dish.
Add Soda: Carefully pour the 7-Up (or equivalent clear, lemon-lime soda) over the dumplings. This addition contributes to a tender texture and a unique flavor in the sauce.
Bake: Bake in the preheated oven for 40 to 45 minutes, or until the apple dumplings are golden brown and the apples are tender.
Serve: Let the dumplings cool slightly before serving. They are delicious warm, perhaps with a scoop of vanilla ice cream!