Preheat the oven to 350°F or 175°C and butter an 8-inch square baking dish. Separate the crescent dough into eight triangles.
Place one apple wedge at the wide end of each dough triangle. Roll the pastry around the fruit and tuck in any loose edges.
Arrange the wrapped apples in the baking dish with a little room between them. Keeping the seam underneath helps the rolls stay closed.
Melt the butter in a small saucepan, then stir in granulated sugar, brown sugar, cinnamon, and vanilla. The mixture can remain slightly grainy.
Pour the butter sauce over and around the dumplings. Slowly add the soda around the outer edges, avoiding the tops as much as possible.
Bake for 32 to 38 minutes, until the pastry is deeply golden and the sauce is bubbling. Cool for 5 minutes before serving with spoonfuls of sauce.
