Mind you I have zero first hand successful experience on cookware but in school they had us weld cast iron test pieces in a couple of courses, once using oxy-acetylene (this is really brazing) and once stick welding. Cookware is usually gray cast iron, which is the type we practiced on.
For arc you'd use a high nickel electrode. Lincoln recommends 55Ni in their guidelines:
https://www.lincolnelectric.com/en-us/support/welding-how-to/Pages/welding-cast-iron-detail.aspx
https://www.lincolnelectric.com/ass...ickElectrodes-Softweld-Softweld55Ni/c8059.pdf
They also make 55Ni in MIG wire but even just a 2 lbs spool is $150.
Using oxy-fuel filler you'd want an RCI filler:
https://www.brazing.com/Pdf/castiron/RCI.pdf
https://www.amazon.com/RCI-Welding-Cast-Iron-Repair/dp/B01D91WGI0 (out of stock naturally)
Success is completely how much time you take to clean and prep. Grind the crack into a bevel then clean, clean, clean. We pre-heated the whole piece. Pre-heating will be tricky since you'd have to be careful heating a pan hot enough (which is ideally 1,000°F) without warping it. So I'd go close to the minimum (usually 500°F) and be careful not to put in more heat than necessary while welding.
The school had ovens to control the heating and cooling rate. The AWS has a specification for it, like 200°F/hour or something like that.
I bet you could put it in a kitchen oven to pre-heat well. Our oven will get to 550°F anyway. Put it in cold and let it go at max for a while to make sure it's completely soaked. Then put the piece back in after welding, turn the oven temperature down over the span of a couple of hours. Kind of like you'd do when seasoning it.
Most people use a torch to pre-heat, that's the way it's been done since Moses first struck an arc anyway. Controlled cooling then being done by leaving it buried in the kid's sand box all day. Being a family heirloom I'd at least try to do it scientifically, even if it's just kitchen DIY science, though.
In theory you could knock the flux off a 55Ni stick and use it to TIG but I'd be careful trying to TIG because the heat would be awful focused, which is just what to do not want with cast iron. OTOH you could control it well, precise and quick. Maybe do the crack in a couple of cycles.
There's the universal silicon-bronze fillers. That almost always sort of works to TIG anything to anything. It's sort of high temperature brazing, not quite really welding.
Me? I'd call John Henley, at least for advice.
Good luck!
