Preheat the oven to 350ºF, and lightly butter your pie plate or casserole dish.
In a small bowl, mix together the self-rising flour and Greek yogurt until combined. Turn it out onto a well-floured surface. Press it down and fold it 13 times, rotating a quarter turn with each fold. Roll it out into a 6-inch by 12-inch rectangle.
Brush the dough with all of the melted butter. Then sprinkle the cinnamon and sugar evenly over the entire rectangle. Working from the long side of the rectangle, roll it tightly into a log. Cut into 6 even rolls.
Place the rolls into your prepared dish, and bake for 15-20 minutes until very lightly browned.
For the frosting, break up the softened cream cheese with a fork, pressing it against the sides of the bowl and scraping it down to soften it further. Sprinkle in the powdered sugar 1 tablespoon at a time, whisking it in until no lumps remain. Then, flavor with vanilla and salt. Finally, thin it out but gently and slowly whisking in the milk.
Allow the cinnamon rolls to cool for 5 minutes before dressing with your frosting. Serve immediately after adding the icing.