I've enabled Azure AD Domain Services under Active Directory > Configure, so that I could decommission the Domain Controller VM I have been running in Azure the past year.
After an hour or so, it generated two IP addresses for the Domain Controllers. As per the instructions, I replaced the DNS settings for my Virtual Network with these two IPs and rebooted one of my Azure VM's. Sure enough, it picked up those two DNS servers from DHCP.
But now...that Azure VM can't resolve any of my on-premises hosts.
I have my on-premises network connected to Azure via ExpressRoute.