I'll speak for one Midwesterner, me.
First, as I've made plain here many times, I have zero use...no, make that negative infinity use for any kind of dictate as to what is and isn't an authentic this, that, or the other.
Second, when I make a butterburger, first I dice butter into fairly small cubes, and that goes into the raw ground beef, a 1/4lb butter for a pound of 80/20 beef.
That gets worked together a bit, then pattied and fried in a pan, no grill. That's because the butter will escape on the grill. Heat up the cast iron skillet in a medium oven, throw in a couple of tablespoons of butter, then the burger, then back in the oven for a bit (think reverse sear), and when I flip the burger, another tablespoon or so of butter sat on top of the patty, just to melt in.
Once it's cooked the way I like it, I take it out, wipe out the pan, heat it on high, and a quick sear on each side. Then, while the burger is rest, I add more butter to the skillet, off the heat, and then put the buns in to toast/fry in the butter.
But wait, we're not done yet. Once the buns come out, I pour whatever burger juices have accumulated back into the skillet with a bit more butter, heat that back up a little to come together, then pour that back over the burgers, then build from there.
There are a lot of different prep methods for butterburgers. Some are no more than just slathering on some butter, like a condiment, and some try and go upscale with the compound butters and such. I keep mine simple: add butter to the meat, fry in butter, toast the bun in butter, and finish with a little butter sauce.
