Prepare for It. Like the situation above, you should go into the conversation knowing how you'll respond if your boss asks you to extend your notice. If you've landed another job offer and have already set a start date, this may not be possible__so practice sticking to your guns: "Because I have a new opportunity lined up, my last day here is firm.
Why a Resignation Letter? In these digital times, why should we submit a resignation letter, anyway? A paper trail does seem old_fashioned, but in this case, it's a best practice. It makes your intentions clear, as well as the conditions. You're removing any ambiguity about the end of your time there.