Modern Vespa

How would one go about removing this big castle nut?

i would get the correct tool.

https://www.sip-scootershop.com/en/product/castle-nut-tool-sip-for-castle-nut-bearing-driveshaft-for-vespa-125-vna-vnb-gt-1-gtr-1-150-vba-vbb-vgla-b-gl-sprint-1-v-1-180-rally_25276600?q=vbb%20tool

and since someone went in there with a punch, i would buy a new retainer.

https://www.sip-scootershop.com/en/product/castle-nut-bearing-driveshaft-for-vespa-125-vna-vnb-gt-1-gtr-1-150-vba-vbb-vgla-b-gl-sprint-1-v-1-180-rally_21104150

anything worth doing is worth doing right.

I like this one instead-

https://www.sip-scootershop.com/en/product/castle-nut-tool-bearing-front-wheel-drive-shaft-sip-for-vespa-160-gs-180-ss_25276700

Works for your bike as well. This one you can use without having to take the driveshaft out. For the future when you gotta replace that seal again.

Cut up an old steel ruler or piece of flat bar and clamp vice grips to it for a handle or tap tap tap it slowly around with a flat punch or old screwdriver. Careful this tends to distort the teeth.Good luck

Isn't it also reverse threaded?

IIRC, yes. Reverse thread.