In a large bowl, combine flour, yeast, salt, and sugar. Cut in butter as would be done for pastry dough.
In a separate bowl, combine beaten eggs, vanilla, and scalded milk. Mix together to combine wet ingredients. Add wet ingredients to dry ingredients and mix together. The dough will be very shaggy and wet. If worried, do not fear! It is unlike any other yeast dough.
Once mixed together, cover the bowl tightly and place it in the refrigerator for at least eight hours (up to 10 hours). Once the dough has rested in the refrigerator, it will have risen slightly and be much easier to handle.
When ready to make cookies, in a bowl, mix together brown sugar, and cinnamon and set aside.
On a lightly floured surface, separate dough into three sections. Working with one section, roll into a 12x15 inch rectangle. Sprinkle evenly with ⅓ cup of brown sugar and cinnamon mixture, leaving a one-inch border on the long side.
Roll up as you would cinnamon rolls or a jelly roll. Slice into one-inch cookies and place on a greased cookie sheet. Press lightly with floured hand and place into preheated 350°F oven for 8-10 minutes. The cookies will puff and brown slightly.
Once baked, let cool five minutes on pan then remove and place on a cooling rack.
For the frosting, combine all the ingredients and mix at high speed until smooth and creamy. Frost the cookies while they are still slightly warm so they are coated evenly.