Burgers are perhaps the easiest thing in the world to sous vide... they only take 30 minutes at temperature to cook through, so you can easily do them in a beer cooler... and then it's 45 seconds per side to get your crispy crust and melt your cheese and you're done. So not much of a recipe here, but some tips instead. Kenji says not to use any added fat like butter (dilutes the flavor) during the sous vide process, but that aromatics can go in the bag with the meat (like garlic and parsley) for a little added flavor. Thus I made roughly 6 ounce patties and seasoned them liberally with salt and pepper and then put them with some sliced garlic in cheap little sandwich bags, instead of those hand pump bags, to save a little money. Then I just dunked them in a bowl of water as I sealed them up to force out the air. While this helps keep the burgers from getting overly squished by the vacuum pressure, they're going to have a lot more air in them (thanks to the ground meat) than a steak or chicken breast sealed up with this method. This makes them a bit more buoyant, so you have to be careful to make sure none of the burgers end up floating on top your sous vide water bath. I had the water preheated to 130 degrees F for medium rare, and that's about all there is to it. Dry the patties thoroughly, heat up some vegetable oil to smoking, and then pan fry for 45 seconds a side. Done.
Next time I will probably try deep frying them. The argument against deep frying is that by the time you get your nice crust you'll have a thicker layer of overcooked meat than pan frying. The pro argument is that the crust is uniform around the entire burger. I also feel like it would be a lot less messy... believe it or not... as pan frying gets oil and smoke everywhere (to say my vegetarian wife is not a huge fan of "burger night" because of this would be a massive understatement), which would largely be missing with deep frying. You have a giant pot of dangerously hot oil to deal with obviously, but I don't find that to be too daunting at this point.
Something to try for 4th of July for my fellow city dwellers with no access to grills.