Mix shortening in the flour with stand up mixer with paddle shape attachment (you can also use a standard mixer). Mix until fully combined together. Add 1 cup of milk and mix until all ingredients are moist. Turn dough out onto floured surface and knead lightly or use dough hook attachment and knead lightly.
Roll dough out until about 1/3-inch thick and then spread the softened butter on the dough; leave a 1/3 inch border around sides. Combine both of the sugars and cinnamon and mix well. Sprinkle over the butter mixture and massage it into the butter well. Start rolling the dough tightly and press the edges and ends together. Cut into 1-inch slices and place cut side down on a greased cookie sheet. Bake for 20 minutes. Drizzle glaze over hot cinnamon rolls and enjoy!