Queen of the Highway is the final Side Job in Panam’s Side Job questline, and it will begin shortly after you finish With a Little Help from My Friends. Just drive a short distance away from the Aldecaldo camp and skip forward a day and you should get the call from Panam that starts the quest. She’ll invite you over to test ride the basilisk. Who doesn’t want to play around with a tank?
Return to the Aldecaldo camp and talk to Panam, and after some chatter, climb into basilisk. Panam will talk at you and eventually get the machine started, and when you’re in control, just drive forward to the first quest marker. After that, Panam will tell you to steer around some wind turbines. You don’t need to be quick or clever here, just hit the markers as they appear. Finally drive to the indicated location and Panam will switch from pilot mode to gunner mode, allowing you to finally do what you came here to do - use the main cannon to blow up some junked vehicles.
Destroy them all and Panam will jack in, the results of which will vary wildly depending on whether you can romance her or not. If the romance possibility is still alive, you can seal the deal by picking the option [Let Panam touch you] “Oh yeah. Let’s go.”. If not, not.
Either way, your playtime in the basilisk will be interrupted by the appearance of some Raffen Shiv, who are attacking the Aldecaldo camp. Unfortunately for them, Panam’s decision to steal the basilisk was an inspired one, as you’ll prove when she sics you on the Raffen. Shoot any vehicle you see as you follow the quest trail back to camp, and when you arrive you’ll find a whole line of targets waiting for you. In the realm of squabbling nomad clans, a piece of corpo tech - even an outdated cargo tank like the basilisk - is overwhelmingly powerful.
Suffice to say, you should be able to casually dust them all without any trouble whatsoever.
Pile up the required number of Raffen corpses, then head to the designated location and exit the basilisk. Wait for Panam and she’ll chat with Saul, then follow her as she talks and request whatever drink you wish when you reach a bar. Respond however you wish to her proposition and you’ll be interrupted by another relic malfunction. When you recover, chat with Panam some more (again, your choices don’t matter) then after being interrupted by Mitch and Saul, walk and talk with Panam some more. Once you’re finished talking with her, the quest will end, and with it, Panam’s Side Job questline.