The requirement is for workloads inside a VPC to resolve private DNS names that are hosted on-premises over a VPN connection. The most secure and AWS-recommended method to achieve this is to use Amazon Route 53 Resolver outbound endpoints with forwarding rules.

Option A enables DNS queries that originate in the VPC to be securely forwarded to on-premises DNS servers through the VPN connection. A Route 53 Resolver outbound endpoint provides elastic, managed DNS forwarding capability without exposing DNS services to the public internet. By creating a Resolver rule, the company can define which domain names (for example, internal corporate domains) should be forwarded to specific on-premises DNS IP addresses. Associating the rule with the VPC ensures only authorized VPCs can use this resolution path.

Option B is used for the opposite scenario: when on-premises systems need to resolve private DNS names hosted in AWS, not when AWS needs to resolve on-premises names. Option C is invalid because Route 53 private hosted zones can only be associated with VPCs, not directly with on-premises networks. Option D is insecure because it exposes internal service records publicly and violates the requirement for private DNS.

Therefore, A is the most secure solution because it keeps DNS resolution private, uses managed AWS infrastructure, integrates cleanly with VPN connectivity, and follows AWS hybrid DNS best practices.