Heat the oil a wok or large skillet or wok over medium-high heat. Add the ginger and garlic and cook, stirring, until aromatic but not brown, about 30 seconds.
Add the cabbage and carrots and cook, stirring, until wilted, about 1 minute.
Add the shrimp, scallions, mirin, soy sauce, pinch of salt and pepper and cook, stirring, until the shrimp turn pink, about 2 minutes.
Remove from the heat and stir in the sesame oil. Let the mixture cool for 5 minutes. Fold in the bean sprouts. Leave to cool another 10 minutes, then chop the mixture evenly and set aside.