Preheat the oven to 350°F. Lightly grease a 9-inch round baking pan.
In a medium bowl, mix together the pumpkin purée, brown sugar, softened butter, pumpkin pie spice, cinnamon, and salt until smooth and combined.
Carefully unroll each cinnamon roll into a long strip of dough, keeping the cinnamon filling intact.
Spread a layer of the pumpkin filling over each strip of dough.
Starting with one strip, roll it into a spiral and place it in the center of the prepared baking pan.
Continue wrapping the remaining strips around the center spiral, connecting the ends to form one giant cinnamon roll. Use as many strips as will comfortably fit in the pan.
Bake for approximately 25 minutes, or until the top is golden brown and the dough in the center is fully baked. If the top browns too quickly, loosely cover it with aluminum foil and continue baking as needed.
Allow the cinnamon roll to cool slightly before drizzling the included icing over the top.
Slice and serve warm!