When the sweet dough has completed its first rise, place it on a generously floured surface. Gently roll it out to a 12 x 14 inch rectangle, about 1/4 inch thick.
Spread the softened butter across the dough, then sprinkle the brown sugar evenly across the surface. Next, sprinkle the cinnamon on top of that.
Roll the rectangle snugly into a log. Pinch the seam shut and place the log seam-side down on a flat surface.
Using unflavored dental floss or a serrated knife, gently slice the log into 8 to 10 rolls, a little more than an inch wide.
Place the rolls cut-side down into a 9-inch pie dish that has been lightly buttered. Leave an inch or so between rolls for them to expand. Cover loosely with plastic wrap or a damp dish towel and let rise until the rolls are puffy and fill the pan- about 1 hour.
Preheat the oven to 350 degrees F. When the rolls have finished rising, bake them for 20 to 22 minutes, until lightly golden on top.
While the rolls cool, make the frosting. Beat the butter and cream cheese together until smooth. Add the confectioners sugar in batches, beating vigorously after each addition until smooth. Finally, add the vanilla. If you'd like more of a glaze, add milk 1 tablespoon at a time until it reaches your desired consistency.
Spread the glaze over the rolls while still slightly warm to let the frosting melt into the cracks. Enjoy immediately!