Bring a medium pot of salted water to a boil. Stir in the rice and boil until just done, about 10 minutes. Drain the rice and set aside to cool.

Meanwhile, in a large nonstick frying pan or wok, heat 1 tablespoon cooking oil over moderately high heat. Add half the mushrooms and cook, stirring frequently, until the mushrooms are tender and golden, about 5 minutes. Transfer to a plate. Repeat with the remaining mushrooms and another tablespoon of the cooking oil. Add these mushrooms to the plate.

In the same frying pan, heat the remaining tablespoon of cooking oil over moderate heat. Add the red pepper flakes, ginger, and scallions and cook, stirring, until fragrant, about 30 seconds. Increase the heat to moderately high and add the rice, salt, and soy sauce. Cook, stirring, for 2 minutes and then add the peas and mushrooms. Cook, stirring, until everything's warm, another 1 to 2 minutes. Remove the pan from the heat and stir in the sesame oil.