Big update in the Menendez Brothers case ... California governor Gavin Newsom just revealed when Erik and Lyle will appear before the parole board.

Gavin dropped the bombshell news Tuesday on his new podcast, announcing the convicted killers will go in front of the parole board June 13 for a hearing.

The Governor says after the hearing, the parole board will finalize their risk assessment and send it to his desk ... and he'll consider their findings as part of his decision on whether to grant clemency in their case, which would set them free.

Erik and Lyle have another path to freedom here ... Gavin says the risk assessment will also be sent to the judge for possible resentencing ... and a lighter sentence could spring them from prison too based on time served.

Los Angeles County District Attorney Nathan Hochman is on the record saying he doesn't think the brothers should be resentenced, but Gavin's circumvented the D.A. and it looks like there's a real shot Erik and Lyle are finally freed.

We've broken down their case and bid for freedom on our new podcast, "2 Angry Men," and it will be interesting to see if the parole board rules they no longer pose a danger to society and sets the wheels in motion for their release.

It's all coming to a head soon ... so stay tuned.