do you play Fenders or Gibsons? A Gibson 54-58 reissues would have pretty substantial necks. I think Fender reissues from the same years would be pretty fat as well.
It's a fat neck, but it depends on what you are looking for, my Baja has a thinner nutwidth than my other guitars which have thinner neck profiles, so it's a baseball bat, everywhere but the top 3 frets, which is my only gripe about that guitar.Fender Baja Tele is a good place to start. Those should be fairly easy to track down.
You didn't indicate your price point, so I know know whether '58 or '59 Reissue LP is in your ball park, or not, or a Core PRS, etc. And there are different levels of "thick"...what some consider thick, others might find it too thin. But, from my perspective as someone who does like fat neck guitars, here are some thoughts.
The '58 and '59 LPs are, by many standards, thick necks. I've had a '58 RI and it was one of my favorite neck profiles. But those two will probably run $2500+ on the used market. I haven't tried a Nocaster, but they're also pricey and not readily available at most of the guitar shops I frequent. On a more modest price point level, I have found the Baja Tele neck to be one of my favorites, and many PRS (Core and SE models) that have, for me, very comfortable wide fat neck profiles. I currently have a PRS Grissom and an SE Bernie Marsden...I actually prefer the Bernie's neck...slightly wider and thicker. I could go on, but those are some starting points for me.
Fender Nocaster