The shell bone script of character Supervise is
The left is character Utensil - 皿 （Post 144), the right is character Meet - 见（Post 201). A person is watching the utensil, which may have some food being cooked. 《象形字典》- Dictionary of Pictography explains "The person is looking himself at the water surface in utensil which is used as a mirror in ancient China". It is possible but from the script above, the person is on the side of the utensil, not in the position where he could see himself in the water surface at all. Besides, Supervise is to watch someone or something else not himself.
Why is watching the utensil with food Supervise? Because in ancient time, food was not enough, so cooking food is very important, the cooker had to cook the food very well to avoid any wasting by checking the food in the utensil constantly.
The bronze script of the character is
A person is checking the food in the utensil. It is very similar to character Face or Facing - 临 (Post 422).
which is a person checking the seedlings.
The big seal script of the character is
The small seal script of the character is
The eye becomes two vertical lines which is lost the pictography completely in order to reduce the strokes. The person on the top right and the utensil on the bottom are unchanged.
The Pinyin of the character is Jian1.
监 means Jail as a noun, which is as popular as Supervise as a verb.