Nick, remember the old serenety prayer? Grant me the serenity to accept the things I cannot change; courage to change the things I can; and wisdom to know the difference.
That's not a prayer just for AA members.
Look. You are ahead of the game. You know that the restaurant has a bad reputation and you know why. You know that you you are better than this, and that they could do better. That's clarity. With a burn-out, you might not know the difference, and feel like you were a bad cook.
The question now is, am I capable of accepting the situation for the continuation of my income and benefits? Or, do I take the risk to talk to the owners about an action plan that would turn things around both for the business and for you. Or do you simply cut your losses and leave.
Whatever you decide, try to separate business from your personal life. Remind yourself that your job only defines who you are when you're at work. This will help you not to take things personally and stay objective. There will always be jobs for good cooks and if you have to leave, then leave. It's all a matter of perspective; if you feel like you're in a deep hole, it makes climbing out very difficult.
If you're worried about burnout, see a doctor. There are a wide range of symptoms including irritability, fatigue, withdrawal, a sense of paralysis, anger. Some people become workaholics while others spend their days shuffling about without accomplishing anything. Whatever the symptoms, you are simply not yourself.
Take care of yourself. You have our support.