Cook the eggs by placing them in a large covered pot (preferably in a single layer.) Add enough water to cover by an inch or more.
Bring just to a simmer, then turn off the heat, cover the pan, and let it sit for 15 minutes.
Remove one of the eggs (re-cover the pot) and run cold water over it briefly until it can be handled, then crack it in several places and peel it under cold running water.
Cut the egg in half lengthwise; if the yolk is a uniform pale yellow, the eggs are done. If it's still a dark yellow in the middle, give the remaining eggs a few more minutes.
Transfer the eggs to ice water until cooled, then peel and cut them lengthwise. Gently scoop out the yolks into a bowl (reserve the white on a plate or platter) and mash the yolks thoroughly with a fork.
Add the celery, scallion (white part), Old Bay, cayenne, and mayonnaise. Mix thoroughly and add more seasoning and/or mayo if needed (you want a well-seasoned, creamy mixture.)
With a sharp knife, carefully cut each shrimp in half lengthwise, so that you end up with 24 'sides' of shrimp.
Place a shrimp over the flat part of each egg white half (so that it curves around the hollow part), and fill the hollows with the yolk mixture using a spoon or piping bag
Cut the green parts of the scallions at an angle into very fine slices and sprinkle over the shrimp. Dust the yolks with a bit more Old Bay and a few grinds of black pepper, if desired.