The initial setup is the same as the article I wrote about Ubuntu 18.10 (create private adapter).

This time, because Ubuntu 19.04 has added something called cloud-init, there’s a new place (yay) to do configuration, however, this time I got it done entirely CLI. Yay me:

mgaudet@ubuntu1904vm:~$ cat /etc/cloud/cloud.cfg.d/50-curtin-networking.cfg 
network:
  ethernets:
    ens33:
      dhcp4: true
    ens38:
      dhcp4: false
      addresses: [192.168.77.15/24]
      gateway4: 192.168.77.2
  version: 2

I added the ens38 stanza above; ran sudo cloud-init clean -r, the machine rebooted and we were done.

Thanks to veprr on askubuntu.com