In a medium skillet over medium heat, cook the onion, carrot, garlic, and mushrooms in 1 tbsp of the oil for a few minutes. Add about 1/2 cup of the chicken broth, bring to a boil, then remove and set aside.

Heat the remaining safflower oil in a saucepan over medium heat. Add the rice, stirring constantly until all kernels are coated. Add the rest of the chicken broth, tomatoes, green chilies, reserved vegetables, salt, and pepper and bring to a boil. Reduce the heat to low, cover and cook, undisturbed, about 20 minutes or until all the liquid is absorbed and the rice is tender. Stir gently and serve immediately.