Melt 3 tablespoons of unsalted butter and brush it over the foil-covered rolling pin to prevent sticking.
Divide the risen dough into 4 equal pieces, each weighing a little less than 4 ounces.
Roll one piece of dough into a long rope approximately 2 1/2 feet long and 1/2-inch wide.
Starting at one end of the prepared rolling pin, tightly coil the dough rope around the rolling pin 4 to 5 times, ensuring to tuck and pinch the top and bottom of the rope onto itself.
Repeat the coiling process with a second piece of dough on the other side of the rolling pin, without overlapping the dough strips.
Use gentle pressure to press the strips of dough together by rolling the rolling pin lightly on the work surface.
Brush additional melted butter over the surface of the dough.
In a small bowl, whisk together granulated sugar and ground cinnamon. Sprinkle this mixture over the dough, rotating the rolling pin to coat the dough evenly.
Place the foil-covered rolling pin on a 9×13-inch baking pan, resting the handles on the short sides of the pan. Bake the chimney cakes for 10 minutes until they become slightly puffy and golden.
Remove the pan from the oven and rotate it to ensure even baking. Continue baking for another 10 minutes or until the chimney cakes turn golden brown.
Once baked, microwave the remaining 2 tablespoons of unsalted butter until melted. Brush the melted butter over the baked chimney cakes and sprinkle them with more cinnamon-sugar.
Allow the cakes to cool slightly before carefully sliding them off the rolling pins. Let them cool further before serving.