That's not nearly as bad as it looks. You can just butt-splice the wires back onto the OEM socket where they cut it and you should have a functional halogen headlight back. But it IS piss poor installation since there's absolutely no need to cut that wire.
CANBus vs. Relay: The Veloster Turbo appears to send a pulse width modulation signal through the headlight (which sits on a CANBus) that drives the relays crazy. If you go the relay route, you'll need to install a capacitor on the relay in order to prevent it from buzzing and self-destructing (since the relay will open and close rapidly due to the PWM signal). The circuitry on the CANBus headlights are robust enough to drive the high-voltage ballast, so a stand-alone CANBus error canceler harness or some sort of CANBus harness with built-in capacitor and resistors to even out the PWM voltage modulations will be more than sufficient to supply power to the ballast and lights. And there'll be far less wiring to deal with (the CANBus harness plugs into the OEM headlight power out, then plugs into the ballast/igniter combo) and will be a far cleaner install. With the CANBus harness I can still remove the entire headlight assembly by disconnecting the headlight harness only*.
*Except I installed the Ballast on a bracket far away from the wheel well, so I'll need to disconnect the ballast too...But IF I wanted to, I could have installed the ballast onto the bottom of the headlight housing and the entire headlight could be removed with simply disconnecting the main headlight harness.
