Learn French: Il surveille la casserole tout en cuisinant. - He watches the saucepan while cooking.

Both en cuisinant and tout en cuisinant mean "while cooking," but adding tout emphasizes the simultaneity of the two actions. It highlights that he is doing both things at the exact same time.

Could tout en cuisinant refer to someone else doing the cooking while he watches?

No. A strict rule for using en or tout en with a present participle is that the action must be performed by the subject of the main verb. Here, Il (he) must be the one doing both the watching and the cooking.

Is casserole a false friend here?

Yes! In French, une casserole is a saucepan (a metal pot with a long handle used on the stove). The English "casserole" (a baked dish) would usually be called un plat au four or un gratin in French.

Why use surveille instead of regarde for "watches"?

Regarder simply means to look at something. Surveiller means to monitor or keep an eye on something to make sure nothing goes wrong, which is exactly what you do when watching a pot on the stove so it doesn't boil over.