With kitchen shears, cut through the shell of the shrimp down the back to the tail. Remove the vein and rinse them well. Butterfly the shrimp by cutting almost all the way through the shrimp with a knife. Pat dry and set aside.
Heat 2 inches of peanut oil in a wok or deep skillet to 375 degrees F.
While the oil is heating, whisk the eggs and club soda together in a large bowl. Whisk in 2 cups cornstarch making sure to get out any lumps. The batter should be the consistency of heavy cream. Season generously with salt and pepper - remember it is called Salt and Pepper Shrimp!
Put the remaining cornstarch on a platter and season it well with salt and pepper. Working in batches, dredge the shrimp in the cornstarch and shake off any excess. Dip the shrimp in the batter and let the excess batter drip off. Slide the shrimp into the hot oil and cook about 3 minutes until golden brown, turning them once during cooking. Remove and drain on paper towels. Scoop out any floating bits of batter from the oil, they will burn. Season the shrimp with salt and pepper while they're still hot and put them onto a serving platter.
When all the shrimp have been cooked, carefully pour out all but 2 tablespoons oil into a safe container. Add the chilies, garlic, and ginger and stir-fry for about 1 minute. Take the wok off the heat and pour in the soy sauce and sake. Cook for 1 minute, then pour this mixture over the fried shrimp. Garnish with cilantro.