It is possible to create Hyper-V virtual machines (VMs) that run on a Hyper-V server in Azure. The key enabler here is Azure VMs which are "Hyper-threaded and capable of running nested virtualization". Only certain VMs have this capability and are listed here https://docs.microsoft.com/en-us/azure/virtual-machines/acu
The term "nested virtualization" is used because an Azure VM is itself running on a Hypervisor. Therefore, running a VM on a machine, which is already itself, running on a Hypervisor is referred to as being nested. https://azure.microsoft.com/en-us/blog/nested-virtualization-in-azure/
There is nothing special* about a nested VM and no special configuration needed to run them. It is just a normal VM running on a Azure VM which is capable of running "nested" VMs.
At this point I'll make a particular and important note. Hyper-V servers can create three types of virtual switches to enable the guest VMs to have a network connection. External, Internal and Private. External virtual switches are not allowed on Azure Hyper-V servers.
To fire up VMs with network connections on an Azure Hyper-V server, create an internal virtual switch and use NAT to give the VMs connectivity to the internet. Private virtual switches only allow the connected VMs to see each other and nothing else.
On this very useful link Cheng (Charles) Ding describes the process of configuration NAT with powershell and also using the option of configuring a DHCP server to automatically assign selected IP addresses. It is possible to add the DCHP server role to the Hyper-V server but it is important to remember that if the server is a member server on an Active Directory domain, the DHCP server must be specially authorized in the AD before it is able to do its job. This tasked can be accomplished in the DHCP applet by selecting DHCP and then using the menu item Action_Manage Authorized Servers.
Finally a note on the powershell script to create nested VMs on Cheng's page. I did not use or test the script. The script is not activating anything special related to nesting. It appears to be a way to automate the spin up of a nested guest VM on an Azure VM that is capable of running "nested" VMs. The same result can be achieved "manually" by running through the procedures to add the Hyper-V role, create the virtual switch, vm, etc
Additional useful reference and discussion of more advanced network configuration.
https://www.jeffgilb.com/hyper-v-nested-vms-in-azure/
*It is a bit special. Running VMs on VMs is cool and there were probably some technical hurdles for Microsoft to overcome before this became possible.
