Preheat oven to 350°F and grease a 9 x 13 baking dish.
Slice peaches so you have 16 large slices.
Separate the crescent roll dough into triangles.
Roll a peach slice in a crescent roll triangle starting at the largest end and place in baking dish. Don’t worry if your peach slice isn’t completely covered by dough.
Melt butter in a microwave safe bowl or large Pyrex measuring cup.
Add sugar, cinnamon and vanilla extract, stirring well to combine.
Pour over the top of peach dumplings.
Pour 2/3 of a can of ginger ale between the dumplings and along edge of pan so the sugar/butter mixture stays on top of dumplings.
Bake for 35 - 40 minutes or until golden brown.
Remove from the oven and let stand 10 minutes before serving. Serve with ice cream, spooning some of the sauce mixture from the pan over the top.