When I visited Korea last year, egg sandwiches could be found everywhere! I was excited when I saw the first Korean egg sandwich shop open up in Irvine: Flippoly. Since the initial location, they've been opening others in SoCal as well. If you've never tried a Korean egg sandwich, you gotta!
They have many options, but by FAR the best one is the Kimchi Bulgogi sandwich. Don't bother with the other ones even if you're normally turned off by spicy kimchi - the Kimchi is cooked, which neuters the spiciness, and instead becomes an important bitter note to offset all the umami flavors. You'll love it, I promise!