In a scenario where resources must be deployed while complying with a security policy that restricts access to the on-premises network, what should be chosen for the migration?

The most suitable choice for deploying resources while adhering to a security policy that restricts access to the on-premises network would be Azure ExpressRoute.

Azure ExpressRoute establishes a private connection between your on-premises infrastructure and Azure, bypassing the public Internet. This not only enhances security by preventing exposure to the public network, but it also provides higher reliability and lower latency, making it a preferred solution for sensitive data transfer and compliance with stringent security policies. This connection ensures that there is no direct access to the on-premises network, aligning with the requirement for restricted access.

In contrast, Azure Virtual Networks provide connectivity within Azure and can integrate with on-premises environments, but they may still expose certain aspects to the internet depending on configuration.

A VPN Gateway offers a secure connection over the public Internet; however, it wouldn't be the best option when strict compliance with a security policy is essential because it cannot guarantee the same level of reliability and performance as ExpressRoute.

Public-facing virtual machines would typically be accessible from the Internet, which directly contradicts the need for restricted access to the on-premises network, making them unsuitable for scenarios governed by strict security policies.