Heat the oil in a Dutch oven or other heavy 3-quart pot over medium-high heat. Add the mushrooms, red pepper and onion and cook stirring, until the vegetables are softened, about 4 minutes.
Add the rice and the salt and stir to coat the rice with oil. When the rice starts to look "chalky," pour enough water into the pan to cover the rice by 1-inch. Raise the heat to high, bring the water to a boil, and boil until the level of the water meets the level of the rice.
Reduce the heat to very low, give the rice a very thorough stir, and cover the pot. Cook until the rice is tender but with a little bite, about 20 minutes. Do not uncover the pot or stir the rice while it cooks. Fluff with a fork before serving. Stir in the scallions and transfer to a serving bowl.