Preheat your oven to 350. Spray a 9x13 baking dish with nonstick cooking spray.
Slice your peaches. You can leave the peel on or take it off if you prefer. Slice each peach in 4 and remove the pit in the center.
Open the crescent dough and divide at the lines into triangles. You should have 16 peach slices and 16 dough triangles.
Place a peach slice horizontally on the widest end of the dough triangle. Roll up the peach and place it seam down in the baking dish. *I pinch the seam closed a tiny bit. Continue with all of the peach slices.
In a medium microwave-safe bowl, melt butter and stir in the sugars and cinnamon. Stir well until all the sugar is dissolved. Spread the mixture over the dumplings.
Pour the soda around the pan's edges and between the dumplings in the bottom of the pan. *Don’t pour it directly over the top of the dumplings.
Bake for 35 minutes until golden brown on top and bubbly. Remove from oven and let set for about 10-15 minutes for the sauce to thicken.
Serve with vanilla ice cream, and enjoy! Store leftovers in the fridge and reheat in the microwave.