Preheat oven to 425 degrees F. Grease a 13"x9" pan or two 8"x8" pans and set aside.
Put all ingredients, except buttermilk, butter, and cinnamon sugar in a mixer. Mix until shortening is about the size of peas.
Turn mixer on low speed and slowly add buttermilk. Stop mixing as soon as dough comes together. Knead dough a couple of times. Dough should be mostly dry, not overly sticky.
Roll out dough on floured surface to 1/4 and 1/2 inch thick. Spread dough generously with melted butter and cinnamon sugar.
Roll up starting with long side. Pinch seam shut. Cut into 15-20 rolls and place into greased pan.
Bake in preheated oven until lightly golden, about 15 minutes. Cool about 10 minutes before icing. To make icing, add powdered sugar to any extra butter. Mix in enough milk or water to make a glaze. Store covered at room temperature.