Push cooked egg yolks through a fine-mesh sieve to break up, then combine in a food processor with scallion whites, gochujang, miso paste, rice vinegar, mirin, and sriracha. Process ingredients until smooth. Place filling in a piping bag and reserve in the refrigerator for at least 1 hour.

While filling chills, make a standard breading station of all-purpose flour, blended eggs, and panko breadcrumbs that have been lightly seasoned with kosher salt. Dredge hard-boiled egg white halves in flour, then in egg mixture, then in panko breadcrumbs to coat.

Heat vegetable oil to 375 degrees F, then carefully drop breaded egg whites into oil. Fry for 3 to 4 minutes until golden brown. Once fried, drain egg whites on a tray lined with paper towels. Pipe filling into the fried egg whites and garnish with cooked bay shrimp and chopped green scallion tops.