Bring a medium saucepan of water to a boil. Add the noodles and cook until al dente, about 2 minutes. Drain and toss with 1/2 teaspoon sesame oil; set aside.
Heat 2 teaspoons vegetable oil in a 10-inch ovenproof nonstick skillet over medium-high heat. Add the chicken and 2 teaspoons oyster sauce; season with salt and pepper. Cook, stirring, until the chicken is no longer pink, 2 to 3 minutes. Add the coleslaw mix, scallions, remaining 1 teaspoon sesame oil and a big pinch of salt. Cook until the coleslaw wilts, about 2 minutes. Remove the mixture to a bowl and wipe out the skillet.
Whisk the eggs, pickled ginger, 3/4 teaspoon salt and a few grinds of pepper in a large bowl. Stir in the ramen and the chicken mixture. Heat 1 tablespoon vegetable oil in the skillet over medium heat. Add the egg mixture and reduce the heat to medium low. Stir gently with a rubber spatula until the eggs start setting, about 1 minute. Cook, undisturbed, until golden brown on the bottom and almost set on top, 7 to 8 minutes. Invert the frittata onto a plate, then slide back into the skillet and continue to cook until the egg is set, 3 to 6 minutes longer. Transfer to a platter.
Meanwhile, heat the remaining 1 teaspoon vegetable oil in a large nonstick skillet over medium-high heat. Add the bok choy, remaining 1 teaspoon oyster sauce and a pinch each of salt and pepper. Cook until crisp-tender, 4 minutes. Serve with the frittata.