Season the shrimp lightly with salt and pepper. Heat a wok or a large skillet or saucepan over high heat until very hot. Add 1 tablespoon of the vegetable oil, and when it is hot, add the shrimp and quickly stir fry them until they are pink, only about 2 minutes. Remove them to a plate and set aside.
Heat 1 more tablespoon of oil in the same wok or saucepan over high heat. Add the beaten eggs and scramble quickly, sliding them out onto the plate with the shrimp when they are just cooked through, about 2 minutes.
Return the wok to the burner over high heat, add the remaining tablespoon of oil, then add the cooked rice and stir fry, stirring occasionally until it is lightly browned in spots, about 5 minutes. Add the carrots ginger and the garlic and stir until you can smell the seasonings, 1 to 2 minutes. Add the soy sauce, edamame, and scallions and stir until everything is hot and the carrots are tender, 3 to 4 minutes. Add the cooked shrimp and eggs and stir until everything is well mixed and hot, 1 more minute. Serve right away.