It is possible to use a trust on first use (TOFU) authentication method in GnuTLS. That is the concept used by the SSH programs, where the public key of the peer is not verified, or verified in an out-of-bound way, but subsequent connections to the same peer require the public key to remain the same. Such a system in combination with the typical CA verification of a certificate, and OCSP revocation checks, can help to provide multiple factor verification, where a single point of failure is not enough to compromise the system. For example a server compromise may be detected using OCSP, and a CA compromise can be detected using the trust on first use method. Such a hybrid system with X.509 and trust on first use authentication is shown in Simple client example with SSH-style certificate verification.
See Certificate verification on how to use the available functionality.