Made sous vide burgers with a poached egg inside yesterday, in response to a challenge from a friend. The inspiration for the recipe was Dave Arnold's Soup Dumpling Burger.
Attached is the result (please excuse the hasty iPhone photo).
The eggs were cooked in a water bath at 62C for 45 minutes. I then removed the loose white and poached the eggs at ~82C for about a minute to firm up the whites--a trick I picked up from Kenji at Serious Eats.
The burger itself was a shortrib/chuck blend I passed through my grinder. The poached eggs were par-frozen for 30 minutes to make them easier to handle when assembling the burger (in a trial run I didn't notice any appreciable loss in yolk taste or texture with this step @ 30 minutes). I used a 3.5" ring mold to make the burgers. Assembled burgers were deep fried for 30 seconds
@300F to set the exterior and then cooked in ziplocks with butter
@55C for 1 hour. I finished them on the griddle and used a Searzall to melt the cheese on top. Served with ChefSteps thin cut fries (not pictured--but they were delicious!). The effort was well worth it.
