Set the oven to 350°F, coat an 8x8-inch glass baking dish lightly with nonstick cooking spray, and peel, pit, and cut the peach into eight wedges. Aim for similar-sized wedges so the filled rolls bake evenly.

Separate the unrolled crescent dough into eight triangles, wrap a peach wedge from the broad edge toward the point of each triangle, and arrange the rolls seam-side down in the prepared dish. The dough should cradle the fruit without stretching thin or tearing.

Stir the melted butter, sugar, cinnamon, and flour together in a small bowl just until combined, then distribute the glaze over all eight rolls with a spoon. A slightly grainy coating is expected, with cinnamon and flour mixed throughout.

Direct the soda into the gaps between the rolls, keeping it off the pastry tops, and bake for 35 to 40 minutes until golden brown. Look for well-colored tops and bubbling syrup around the perimeter, rather than relying on aroma alone.