Combine brown sugar, sugar, cinnamon, and butter in a small bowl.
Remove top sheet of parchment from dough. Spread filling evenly over entire rectangle of dough.
Cut dough lengthwise into 1 1/2-inch strips. Roll up one strip to make center "roll". Place roll into the middle of a 9-inch iron skillet.
Wrap remaining strips around middle roll, connecting the new end to where the last end stopped, to form one large, continuous roll. (Cut strips in half width wise to make them shorter and easier to handle, if needed.)
Once all strips are wrapped, bake at 375° for 25-30 minutes or until golden and cooked through.