Something along the lines of:

export const vpc = new awsx.ec2.Vpc("custom", {
    numberOfAvailabilityZones: 1,
    numberOfNatGateways: 1,
});

And then creating a cluster with that vpc, and associating the cluster to the task.

I actually just realized that I'm trying to test this via inbound traffic instead of outbound. 🤦‍♂️ I'll improve my test and see if I've actually achieved what I wanted.