Does the server have light-out mgmt? You can upgrade the BIOS via that. That takes care of the host. ESXi updates can be done through a vCenter.

VMware has released a slew of patches that fix vulnerabilities in a number of its products, including vCenter Server, vCenter Server Appliance, vSphere Update Manager, ESX and ESXi. Some of the flaws ...

With Update 3e for VMware EXSi 8, Broadcom is bringing back its free vSphere hypervisor for testing purposes. There are also new features for the USB driver. VMware vSphere 8 is once again available ...