You are not allowed to work "under the table" for tax purposes. If he does not give you a 1099 or W-2, he cannot deduct the expenses on his business return. If you claim the income you received, and there is no corresponding W-2 or 1099 for you, they are going to ask where it came from. They are definitely going to force the employer to pay employment taxes as there is no way they are going to be able to say you are an independent contractor.
But if you made roughly $10,000 or more, you are required to file and they will not understand if you do not do so because your boss wanted to keep it "under the table." At the end of the day, he has his own requirements he is not meeting, but you and you alone are responsible for claiming your own income.
In addition, if you are terminated, you will not be allowed to collect unemployment insurance.
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Schedule C is probably the right answer for you. That is, claim you are a cash business (cook consultant to restaurants), which you apparently are. See a tax professional so you do it right, as you're hanging out legally right now. You are foolish to work under the table, as you forfeit benefits like unemployment compensation, which right now are significant, although perhaps you have no other choice. Your boss is also operating illegally and, I might add, apparently stupidly since if he is caught he is going to be very sorry he did that.
So far, this is free to you. Until you pay a fee, I am not your lawyer and you are not my client, so you take any free advice at your sole risk. I am licensed in IL, MO, TX and am a Reg. Pat. Atty. so advice in any other jurisdiction is general advice and should be confirmed with an attorney licensed in that jurisdiction.