Roll out each Rhodes roll flat with a rolling pin; about 1/4-inch thin.
Combine the cinnamon and sugar in a bowl. Brush or dip each side of the roll with butter, then dip it in the cinnamon-sugar covering both sides. Place some graham cracker crumbs, mini chocolate chips, and mini marshmallows on top.
Fold/roll the cinnamon-sugar dough up and over the s’mores fillings.
Place the rolled up dough seam-side down into a greased 9-inch round cake pan. Repeat with remaining pieces of dough. Cover with greased plastic wrap and let the dough rise to the top of the pan.
Bake at 350 degrees Fahrenheit for 25 to 30 minutes, placing foil on top after 15 minutes of baking to prevent too much browning. Check the dough where the pieces touch to ensure it is cooked through.
Make the marshmallow frosting by beating all the ingredients together in a large bowl with an electric mixer. Put the frosting in a zip-top bag, cut off the corner, and squeeze the frosting over the warm cinnamon roll cake.
Sprinkle the warm, melty frosting with extra graham cracker crumbs and mini chocolate chips.
This S’mores Cinnamon Roll Cake holds its shape best if it cools slightly before being cut. Cover and store leftovers at room temperature up to 3 days.