Preheat oven to 350 degrees.
Mix flour and Greek yogurt together using a mixer with a dough hook. Start on slow and then increase the speed as dough starts to form. You may need to scrape down the sides to get all the flour incorporated. Keep mixing until it forms a soft, sticky dough.Note: If you don't have a mixer, you could also mix the flour and yogurt together until combined. Then flour a surface and knead the dough until a dough forms. Continue kneading for a few minutes. You may need to add additional flour if dough is too sticky to work with.
Flour a surface very well (the dough is very sticky! If you don't flour well, dough may break while rolling into a log!), and add the dough on top.
Flour the top of the dough and then roll it out into a 12 x 8 rectangle.
Once the shape is reached, spread softened butter all over the rectangle.
Mix sugar and cinnamon together and then sprinkle all over the rolled out dough. Then begin rolling the dough tightly to form a 12-inch log.
Using a bread knife, divide the dough into 8 equal pieces.
Place cinnamon rolls into a small baking pan (I used a 23 oz. Corning-ware baking pan) sprayed with cooking spray.
Bake in preheated oven for 20-25 minutes, or until the tops are beginning to brown and the middle of the rolls is set.
Allow to cool for 10 minutes, then top with Greek yogurt icing.