In a mixing bowl (I use this one), mix the 1/3 cup sugar, warm water and yeast. Let stand for 5 minutes while yeast proofs.
Mix in oil, salt, and 3 cups of the flour. Mix for 2 minutes.
Add remaining 2 cups of flour, mixing until well combined. If dough is still too sticky (it should be soft to the touch, but not overly sticky) add another cup or more of flour until it is soft but not sticky. Turn mixer on a medium speed for another 2 minutes, allowing it to knead the dough.
Spray a clean surface with nonstick cooking spray and sprinkle lightly with flour. dump dough out onto the surface. Flip dough so both sides have a light layer of flour on them. Using a rolling pin, roll dough out to be about 16 x 20.″
Smoosh softened (not melted) butter around to coat the dough rectangle. I use my hands for this. Sprinkle brown sugar all over the top of the butter. Sprinkle cinnamon evenly on top of that. **note- I usually just eyeball the brown sugar and cinnamon so use your heart on this one if you want!
Starting on the smaller side, gently roll until your dough is one long (16") rolled tube. Use dental floss technique to cut into 12 evenly sized rolls.
Place on a cookie sheet and place in a warm oven for 20 minutes or so until the rolls double in size. Then crank up the oven to 350 degrees and bake for an additional 20-30 minutes until beautifully golden brown.
While cinnamon rolls are cooling slightly, mix together Icing. Whip butter, powdered sugar, whole milk and vanilla until nice and smooth and delicious. Smother rolls with icing while very warm (not super hot) and enjoy!