I think these guys pretty much covered it.
Personally, I'm trying to approach everything from a food science point of view.
Perhaps that perspective will help you too.
In theory, a crust shouldn't be too difficult to achieve,
you're looking at 2 major factors at play here,
temp and time.
A crust only on forms on a dehydrated product.
Your heat has to be high enough to evaporate to surface moisture as well as overcome all the moisture that gets squeezed out from the inside.
Your temp needs to be:
Min. : High enough to dehydrate the surface and overcome all that moisture
Max : Low enough that you don't burn the outside before the inside is done
Air is a poor conductor of heat. Metal and oil are good ones.
That's why most grilled steaks and burgers won't have an crispy crust, while the areas it contacts the grill grates will be blackened and charred.
You can help this even-ness by giving your patties a light rubbing of oil before the grill.
My preferred method is in the pan to get maximum crispy crust.
- A screaming hot pan (cast iron or carbon steel is preferred as they are non-stick and have a high heat capacity).
- Pour in a generous amount of high heat oil (I use grapeseed oil from Costco)
- Swirl the oil for 5 seconds in the pan to bring it up to temp.
- Meat go in. (Any longer and the oil might catch on fire..... get a lid ready to snuff the flames)
- Flip often, 15-20 seconds (for a flat piece of meat, basting is bullshit and not required for this kind of cooking)
- Remove meat and rest (this way, you can do a batch of 20 burgers
- Pour off 3/4 of the oil, add butter
- Finish the sear in the browned butter for less than 1 minute
This way, you can do multiple batches of cooking, then just do the final sear to finish right before serving.
This is the exact same way I do my steaks.

You can throw some aromatics in with the butter such as rosemary, thyme or garlic. I used sage in this case.