I had no idea what a hubcap burger was before reading the OP. If it’s just a 6" burger, that’s basically a Whataburger. Love 'em, open 24 hours.
So… Any good burger?
Yes. A great burger.
The extra size is just a bonus.
I make burgers like that at home. I buy a one pound steak, trim any visible fat, then grind the meat. I make two 1/2 pound burgers and sous-vide them rare. Then I hit them with a torch to lightly sear the exterior. Delicious.
I’d swear there’s only butter on it about half the time. It may just depend on who’s working the grill and how they read my order*. Also, they switched to a new bun that’s not nearly as good and butter or not, the new ones aren’t all greasy like the original ones that we’ve all loved.
However, for a real butter burger look at Solly’s. Those are ‘butter dripping off your elbows’ burgers. They must use 2-3 tablespoons on each burger. Plus IIRC, you can ask for extra butter and they’ll score the top of the bun and dip it in melted butter.
*A hamburger with ketchup, to some means meat and ketchup. To others it means ketchup, along with the typical lettuce and tomato. Then there’s other people that seem to think ‘hamburger with ketchup’ means I meant to say ‘cheeseburger’.
All the confusion and a busy restaurant, I can understand why, if butter is standard, they punt when they see my order.
I’ve linked to this video before on here, but check out the buttering of a burger at Solly’s here (at 0:35–though it should be linked to the correct time.) It’s crazy. “Not many restaurants use the big dollop of butter we use …” says the owner. Yes, I think that is safe to say. 
O gods, you’ve given me a Solly’s craving again. It’s been about 9 months since my last visit there, I think. OMG OMG OMG
That works out to about 80 sticks of butter, per day, every day. And that’s for a place that’s not exactly slammed all the time. If they were as busy as Kopps, there would be cars backed out on to the road and as often as I drive past it, I don’t think I’ve ever noticed their parking lot overflowing.
Are you sure that isn’t an ingredient?
It’s very popular in Ukraine.
There’s a diner about three blocks from me in Brooklyn that cooks a 1/4 pound burger on a red-hot grill under a metal bowl. The objective seems to be searing the burger fast, getting the interior done to medium-rare, and getting it out to the diner in a very short time.
The bowls have little handles on top, are stacked next to the grill by the front window, and look like they’ve been in constant use for at least fifty years.
Meet you there for lunch someday soon? 
I always mean to go there every time I’m in the Milwaukee area, but the one time I did try, the place was absolutely packed, and we ended up going elsewhere. 
Wish I had remembered a couple weeks ago when we drove up to Elkhart Lake, but we stopped in Sheboygan on our return trip to grab some food at the Charcoal Inn and pick up some meat at Miesfeld’s – now damn those are some good brats!
One of these days…one of these days. It’s definitely on my bucket list. (And, looking at the burgers, may be the last item I check off my bucket list.)
That sounds like the technique used at Sacramento’s famous* Squeeze Burger, home what they call the “cheese skirt”. Although they don’t use a hubcap but a hood that I assume is standard restaurant equipment. See the video on their website for a demonstration of the technique.
*Famous because they were featured on Diners, Drive-Ins, and Dives. Although they had to move from their original tiny location because it didn’t meed ADA requirements since that segment was filmed, and changed their name from Squeeze Inn to Squeeze Burger.
Regarding the OP, I correctly guessed that it was a larger than typical diameter burger. But I was picturing it as a ridiculously huge, finish it in one sitting and it’s free, publicity stunt burger.
You can come too. Or we’ll hit one of the Charcoal Inns in Shebco. Or Randalls, even.
Jimani (in the French Quarter, on Iberville) uses actual, Honest-To-God hubcaps, albeit ones that likely might have been actually cleaner and more hygenic back when they were stolen off of a rusting, broken-down 1955 Buick after Hurricane Camille in the Summer of '69.
Cothams gained its popularity when Clinton was running for POTUS, as it was a favorite lunch spot for him when he was governor. I would characterize the hubcap at Cothams as just okay.
Have seen them, have eaten one! At the Clover Grill in New Orleans. Doubtless the hubcap was shtick, and the same culinary process could have been accomplished with a more specific piece of kitchen equipment, but the burger was delicious all the same.
These larger burgers were the first time I’d encountered high quality burgers with fresh ingredients.
Decades ago there just wasn’t much choice. The small independent places usually offered paper thin patties and the burgers were often boring. I remember when McDonald’s opened in my hometown and was surprised at the thickness of the quarter pounder patty.
Today high end burger places are common. That’s a good thing. 