Secure Boot can do the "ROM" scenario on conventional read-write media as long as your OS is capable of maintaining a chain of trust and enforce code signature checks before execution. The media is technically writable, but any writes would break said chain of trust on subsequent loads and so the malicious code would fail to execute.

If interacting with a remote system, a TPM can also be used to achieve the same (though if you have TPM you'd generally always have secure boot) - in this case, your OS extends TPM PCRs with the hashes of all the components in its chain of trust, and the remote system uses remote attestation to prove that you indeed booted & executed the expected code before granting you an access token which is never persisted.

In the second case, malicious code would still run but would be unable to pass that authentication step and thu be unable to communicate with the remote system. This is suitable if the machine itself is stateless and not sensitive per-se, and the only security requirement is ensuring the remote system is only accessed by trusted software.