Best Burgers Ever

We went and got burgers from Dickson's (short-rib burgers that they had already formed into patties, I'd say the patties were a little over an inch thick), and since neither of us have really cooked plain burgers anywhere but the grill, we took to the internet: http://www.browardpalmbeach.com/restaurants/forget-the-grill-five-tips-for-the-perfect-burger-6398139

Here's what we did:

Ingredients:
Burgers -- probably better to make your own if you buy from anywhere other than Dickson's, there are some tips in the article but he says not to over-manipulate them, and I believe everything this man says now.
Butter
Olive oil
Kosher salt, pepper
Buns
Toppings (we had cheddar cheese, red onion and tomatoes)

Directions:
Pour about a tsp or a little more of salt onto a plate to coat both sides of your burger, using your hand to spread it around and pat it on.  Grind a little pepper over both sides.

Heat your cast iron pan (ours was 12") in a 350-400 degree oven for about 20 minutes (we really winged it since our oven temp is unknowable and we didn't keep track of time very well).  Take your pan out and put it on the stove over medium-high heat and put a little olive oil in the pan.  If it beads up, you're ready.

Put the burgers in.  We cooked for about 4 minutes on one side, I would say -- his directions say when you can see the side start to turn brown, but it was hard to tell so I'd go for 4 minutes for burgers of the thickness we used.

Then, flip the burgers.  Once you flip, put your butter (I used a little less than a Tb) on top to let it melt into the burger.  Andy used a splash of olive oil on his instead and said it was good.  At this point, we relied a little bit on a thermometer because our burgers cooked for longer than the article suggested and were rare to medium-rare.  The internet says 145 degrees for medium rare; we cooked our burgers to about 125 degrees (it was about 5-6 minutes) before putting the cheese on, at which point we covered the pan for about a minute and then they were done.

Serve!