With two physical NICs, one per subnet, you can stick to a single vSwitch and play with pNIC assignment for specific port groups, but you shouldn't do that - too messy and prone to error.
Instead, create a second vSwitch, assign the pNIC connected to 10.x to that new vSwitch, and also connect the second virtual NIC of your VM to the new vSwitch.
And the best approach of all, even though more compicated:
If not done yet, put both subnets on the same physical switch as separate VLANs. Find the two ports on the switch that are used by the ESXi host and configure them as trunk ports. Assign both pNICs to the same vSwitch. Configure two port groups on the vSwitch, and specify the VLAN IDs in the port group configuration. Connect vNICs of your VM to the corresponding port groups. The advantage of this solution is that provides network redundancy where previously every physical link was a single point of failure.