Put yeast in mixing bowl. Add warm milk and sugar. Let rest 5 minutes.
Add flour, salt, and oil, and mix well. Add up to 1/2 cup extra flour if neccessary.
Mix well with hands, spoon, or KitchenAid. Knead until the dough begins to clean the sides of the bowl.
Place dough into a greased bowl to rise. (I just add a little oil to the mixing bowl and turn the dough over once to coat the sides of the dough.)
Let the dough rise to nearly double in volume (about 30-45 minutes).
Place dough on floured counter and roll out with rolling pin to about 1/2 inch thick, in an oblong shape approximately 12x24 inches.
Spread softened butter evenly over the dough. Spread the brown sugar over the dough with your hands, in an even layer. Sprinkle generously with cinnamon.
Starting at the longest side, roll dough up tightly. Slice into pieces about 1 1/2 inches thick. Place into greased baking pans.
Turn the oven on to 350. Let rolls rise while you preheat the oven. Bake for 20-25 minutes, or until the tops turn golden brown. Do not overbake! The tops should be just barely brown. Cool and frost.
Caramel Frosting: Melt butter in pan over medium heat. Add brown sugar and simmer over medium heat for 2 minutes, stirring constantly. Add milk, and continue stirring until it comes to a boil. Remove from heat and whisk in powdered sugar. Pour over warm cinnamon rolls.
Notes
Using bread flour will really make tases rolls super soft! And they will stay soft much longer. Totally worth the small extra cost to buy bread flour.