Cut the antennae and sharp, pointy ends of the shrimp just below the eyes using scissors. Make a shallow incision through the shell and into the flesh along the back, from head to tail. Pick out the vein.
Season the shrimp with salt and pepper, then lightly coat them with cornstarch.
Toss shishito peppers in a bit of oil, then place them in a preheated wok. Let them blister for about 5 minutes over high heat. Season with salt and pepper. Transfer to a plate.
Heat about an inch of oil, enough to cover the shrimp halfway. Test the temperature with a wooden chopstick or spoon handle; if it's steadily bubbling, it's ready.
Fry the shrimp in batches over high heat for about a minute on each side. Don't overcrowd the pan, so they crisp up nicely without overcooking. Add or change the oil as needed.
Remove the remaining oil from the pan and wipe away the browned bits with a paper towel.
Reduce to medium-high heat and add a bit of oil. Sauté 1 tablespoon of ginger and 1½ heads of garlic for about a minute.
Add the peppers and sauté for about 3 minutes.
Add the shrimp and scallions, then toss them together.
Sprinkle some salt and fresh ground pepper.
Arrange the shrimp and shishito peppers in an aluminum pan or a platter of your choice.