How does a general contractor recover money that is still owed to them?

B.B. is right.  You need to get legal advice right away.  This looks to be a small claims case, but construction law is complicated even in small claims.  So if you do go the small claims route you'll need some advice and prep help.  If you are local to the San Francisco Bay Area, I can probably see you today or at least provide a phone consultation.  If you are outside my area, I can probably find you a good referral.

You need to take your contract and the rest of the documentation to a lawyer, now, immediately, as in keep making telephone calls until you find someone who can see you today.

In the first place, it might not be possible for the client to cancel the contract verbally.  I don't know enough about the case to figure out whether it makes more sense to insist that the contract is still in force until it's cancelled in writing, or simply take this as breach of contract and go to settlement demand and then suit.

If the client is found in breach of contract, and can't justify it, you should be able to recover enough to pay all of your actual costs on the job, plus the profit you would have made.  This is called "benefit of the bargain" damages.