Hi,
There are many options available to you for updating VMs running on Azure Stack HCI. The latest option is Azure Update Manager which offers great flexibility to manage both Azure native and on-prem VMs and servers. This specific feature is still in preview, but is the v2 of the current Azure Automation Update Management. It offers many improvements which can be reviewed in the provided links.
If you are looking for PowerShell options, the PSWindowsUpdate module is available for this purpose. I used the simple script below to kick off Windows Updates for VMs running in a test environment.
NOTE: The script below is provided as-is with no warranties or guarantees of support. It is up to you as the user to verify and test the script thoroughly. Microsoft accepts no liability from the use of this script in any form.
$vms = "VM1","VM2","VM3"
foreach($vm in $vms)
{
Invoke-WUJob -ComputerName $vm -Script {
ipmo PSWindowsUpdate; Install-WindowsUpdate -AcceptAll -AutoReboot | Out-File C:\Windows\PSWindowsUpdate.log
} –RunNow -Confirm:$false -Verbose -ErrorAction Ignore}
Hope this helps!