How do I go about upgrading existing Azure VM with Windows Server 2012 to Windows Server 2012 R2?

Specifically for Azure VM. What is the recommended way to upgrade from Server 2012 VM to Server 2012 R2 on the same VM?

I prefer not to have to create a new 2012 R2 VM and really rather upgrade my existing Server 2012 as I have installed different software on it and configurations.

This question was also asked last year per http://social.msdn.microsoft.com/Forums/windowsazure/en-US/15e8a17d-0004-4337-a74d-1aa47df4e92d/server-2012-r2-upgrade?forum=WAVirtualMachinesforWindows and remains unanswered.

In-place upgrades of Azure VMs are not supported by Microsoft.

Ref: https://support.microsoft.com/en-us/kb/2721672

Microsoft does not support an upgrade of the operating system of a Microsoft Azure virtual machine. Instead, you should create a new Azure virtual machine that is running the supported version of the operating system that is required and then migrate the workload.

I realise this might not be all that helpful, but since the Microsoft support position on this wasn't mentioned here, I thought it important to make it clear.