A few years ago in Chicago I had a dish called egg yolk shrimp at a Japanese steak house. Has anyone else had this dish? Where would I be able to find this dish again?
I think you're looking for shrimp with egg yolk sauce. Egg yolk sauce is simply a kind of thick mayonnaise which gets dropped on fried (or deep fried, or grilled) shrimp. The yolk sauce usually has some yellow food coloring in it to make it look more eggy. Using canola (rapeseed) oil helps with getting a nice color too.
It should be dead simple to do at home, you can make the yolk sauce ahead of time, then simply pan fry some shrimp and spoon it on the top. If you are going to bread the shrimp I'd suggest putting the sauce on the side so the shrimp stays nice and crispy.