In a medium saucepan, combine the rice, shallots, chicken broth, and 1 1/3 cups water. Bring to a boil over high heat, stirring. Reduce heat to moderately low, cover the pan and simmer until the rice is tender but slightly chewy and most of the liquid is absorbed, about 45 minutes. Set aside, uncovered.
Fill a medium saucepan with water and add a pinch of salt and bring to a boil. Add the orzo and bring to boiling, stirring, until tender, about 8 minutes. Drain well. Return the orzo to the pan and stir in 1 tablespoons of the olive oil to coat the grains.
*The rice and orzo can be prepared to this point up to 4 hours ahead. Cover and set aside.
Drain the rice and add it to the orzo.
In a large skillet, heat the remaining 1 tablespoons of olive oil. Add the scallions and cook, stirring, until just soft, about 1 minute. Add the orzo and rice and reduce the heat to moderately low. Cover and cook, stirring frequently, until heated through, about 5 minutes.
Season with salt and pepper to taste and serve hot.