For the people who like eggs on their burger, there’s a problem: As soon as the yolk breaks, it runs all over the plate and — thanks to the existence of the whites — the yolk never hits the meat. There’s also a secondary issue of putting eggs inside of meat, as in a scotch egg: in order to cook the egg, one has to overcook the meat (a perfect runny egg yolk temperature sits roughly around 140° F, and a medium rare burger sits around 130° F).
This is the solve for all that. To cook this dish, which nestles an egg yolk inside a burger patty, do so at two different temperatures, starting with the highest first: the egg.
The egg is cooked in a makeshift confit at a higher temp, then placed inside the patty which is cooked at a lower temp. This is achieved through the use of immersion circulators, but could be done easily without with some very precise cooking. The advantage of using sous vide in this method the ability to cook multiple burgers at once. You could hold 10+ burgers in your water bath ready to go for the finish fry, which happens in a matter of seconds. Although the prep seems tedious, most of the time is inactive, meaning you could actually enjoy your party — or finish cleaning up before your guests arrive.