Does anyone have a recommendation for a passive asset discovery tool/appliance?
I've used AlienVault's USM with some success previously.
There are some Open Source tools that are pretty handy, but I won;t suggest any as I'm unsure of current versions and their stability.
It largely depends on what is in your infrastructure, but I won't ask you to disclose that on a public forum.
You should look at Forescout. They have agent less technology that is market leading.
If you are already obtaining Vulnerability Management Services via Qualys, they do Asset Management and discovery: https://www.qualys.com/asset-discovery/
You may find this comes free with the existing service.