Heat the oil in a very large nonstick skillet or wok over a high heat. Add the scallions, ginger and shrimp and cook stirring frequently until the shrimp turn pink, about 1 1/2 minutes. Add the cabbage and continue cooking until it begins to soften, but is still somewhat crisp, about 2 minutes more. Transfer the shrimp-cabbage mixture to a bowl.
Heat the sesame oil in the same skillet or wok over a medium-high heat. Add the rice and cook stirring frequently, until heated through, about 3 minutes. Add the shrimp-cabbage mixture back to the skillet, stir in the soy sauce and sesame seeds and serve.