I think he might be referring to tls sessions. When a client comes back to a server it remembers that it connected to it can send a session Id encrypted with the master secret or a complete session ticket. When the handshake completes successfully you know who it was if you stored that information. It saves using a cookie. Also it might not be supported in every client.

I think you still need to have mTLS or another credential to use initially for auth. Unless I miss an option. As such I don’t see much value over mtls in a corporate network setting.