In the vmkernel log you will see messages about how it fails to add the disk and it ends with "dumping cartel".
In order to be able to access the server through the vSphere client again you will need to restart the server's management agents.
This needs to be done from the local console of the ESXi host which is easiest available through DRAC (or similar). You can find the correct menu under Troubleshooting options.
After situations like these, restarting the agents may take a few minutes.
The reason that adding the local disk crashes is that this server was shipped with a preconfigured disk with several partitions. If we remove these partitions first, these problems will not occur.
From the ESXi's command line (ESXi Shell (troubleshooting mode)) of ESXi we can use partedUtil to achieve this.
There are normally multiple volumes presented to an ESXi host and we do not want to delete the wrong one(s). You may need to run partedUtil against several of your volume IDs before you hit the correct one. You can then delete partition by partition from that volume by using partedUtil delete.
Now you will be able to add the disk as expected.