The requirement is not reasonable. Indicate in your letter that you would like to have been able to give 30 day's notice but due to circumstances you will need to leave in 15 day's time and that you are sorry for the shorter notice.
Short, professional, because it is really none of their concern if and why you are moving forward. State that because of various factors I must terminate my employment on this date and thank them for the time you spent working there. As far as I am concerned (not that you should ever do this) you could just never show up again, and so be it, so giving them written notice 15 days prior to your expected last day is not a problem, that is what they prefer (to have 30 day notice) but you have no obligation to fulfill their wishes.
They can fire you at will . . they cannot stop you from quitting at will . . and the fact that they would like one month's notice . . it cannot be enforce . . . the only thing they can do is reprimand you for not following company rules. Be professional, be nice, write a professional letter and go out on good terms . . if they are mean vindictive people . . .so be it . . they cannot withhold your pay for this . . My guess is you'll be reminded you did not give them their requested time, and you'll be brow beat a bit
Unless you have a specific employment contract, no advance notice is required. Their "policy" does not change that fact.
You simply quit. There is no obligation to continue working for them, just courtesy. Forcing you to continue working would be slavery...
just leave
