There are generally 2 schools of burger patties. Thin and cooked through, and thick and pink. It would help a lot if you explained exactly what you did in your attempt so that we have a baseline.
I’m assuming you went with a thick pink style since you say you burned your burger and got a rare center.
I’m also going to assume you added things to your burger other than meat and salt/pepper. It should be practically impossible to burn a burger patty on a skillet in the time it takes to cook.
A burger is a very simple thing. Start with some fatty ground beef - at least 80/20, form into patties of desired thickness and do not overhandle it. Just put in the least amount of time and pressure into it to form a patty until it just comes together. Salt + pepper goes only on the outside, right before it’s time to cook. Add more salt than you think you’ll need. If your patties are fat, give it a little dimple in the middle, and make sure the sides are vertical and don’t taper off. You want a hockey puck, not a UFO.
Get a pan hot and cook your patty on it. If you are cooking a thick patty, it’s going to need some time. The best way to get it to cook evenly is to flip it regularly. Poke into the patty if you need to in order to check for your desired doneness. I like mine somewhere between medium and medium rare, which probably will take about 7-8 minutes for a 6-8oz lb patty. For a tasty char all around make sure all parts of your patty are making contact with the pan, give it a little press if needed.
If it’s a thin patty, get the pan screaming hot and really press the patty down on it to get the most sear possible in the time you have to cook. 2-3 minutes per side is all you need if you’re working with 1/4lb or smaller patties. The goal here is to get the outside bits of your patty to be practically crunchy.
I like my burgers rare. I grind the meat, weigh out 6 oz portions, form loose patties, and cook them in a lightly oiled, preheated cast iron pan. Three minutes per side is right for me. If one of our guests wants a burger that is less red inside, I make that person a 4 oz burger. That way the cooking time stays the same.
I follow Judy Rodgers’ advice to cut the meat into grinder sized chunks and salt it the night before (about 8 g per kilo of meat). That way they get less handling before going into the pan. I realize that many cooks have come out against pre-salting, but it works for me.
Obviously this is all a matter of personal preference, but loose patties make for a more tender burger and better mouthfeel when you bite into it. Think of how a good burger is different from sausage in terms of density and chew. What makes the sausage dense is pre-salting and compacting, which is what you want to avoid with burgers. Also looser patties give you more surface area to brown.
Anyway, if you added nothing and burned your patty, that means the heat was entirely too high. Honestly I don’t even know how this is possible, unless you heated your cast iron to absurd levels.
Think of it pretty much the same as cooking a steak. A hot cast iron shouldn’t burn a steak on 4 minutes/side, and basically the same thing goes for burgers. If burning is a problem just flip your patties more often and turn the heat down.
Burnt (or heavily seared) on the outside and raw (or close to it) inside is how I like my burgers, LOL. For foolproof and consistent results, though, I find that sous vide makes a great burger. Thick patties compacted just enough to hold together, sous vide for around 45 minutes at 120. They look very unappealing at this point, but all you have to do thereafter is a quick sear on both sides and you have a perfect burger with a rare-med rare center almost edge to edge.
Is there a place that serves your favorite type of burger? Is there a menu description or can you tell us the name of the restaurant or fast food franchise? I’m sure someone here will be able to instruct you in replicating it, so you are able to make what you really like how you like it.
My favorite burger would be medium rare, gigantic, and a bit charred on the outside, but not so much that the surface is crusty hard. I don’t think I can replicate that at home.
I’ve rarely had them. I remember once at a local diner - I’d have to walk past it, it’s at Amsterdam & 67th, I believe. I’ve never eaten at a Shake Shack so I can’t comment.
PS I looked it up on google maps (I can’t believe I did this but…) and the place I had the great burger was the West Side diner, at Bway & 69th. Totally generic name, generic diner, but it was great. A bit charred, a bit smokey, a lot delicious.
The (potentially insane) kenji of serious eats did some crazy testing to get to this thick juicy burger recipe- i haven’t made these myself but there’s a recipe within this detailed how to/why article with his hyper-specific instructions.
And this quick top tips article he wrote has some helpful info too
Basically he is laying out three approaches in the article: flip once, flip frequently, and reverse sear.
He’s saying reverse sear gives you the best results with the most even pink center and decent crust. In a nutshell, 1 flip gives you maximum crust at the expense of a harder gradation in the meat doneness, and reverse sear gives you the most even interior at the expense of more crust. Multi flip is in the middle and my personal method, mostly because it’s the easiest.
In reality all of these methods will yield a good burger as long as it’s executed properly. He also notes that there’s not a big difference in subjective experience between 1 flip and multi flip burgers.
In the end what really matters is that you have a decent fatty patty, get enough browning on the outside to give the patty flavor and texture, and cook it to proper temp.