Spray counter lightly with non-stick cooking spray. Combine rolls and roll into a 12-inch circle. Cut circle into 8 equal wedges. Place an apple slice onto the wide end of each wedge. Roll the dough around the apple slice.
Place the wrapped apple slices in a sprayed 9x13-inch baking dish. Cover the dish with plastic wrap and let rise 30-40 minutes.
Melt butter, stir in vanilla and both sugars. Pour over risen dumplings. Pour soda over dumplings and sprinkle with cinnamon.
Bake at 350°F 20-30 minutes. Spoon syrup from pan over the dumplings to serve.