Combine the chicken broth and rice in a medium saucepan. Bring to a boil, then reduce heat, cover and simmer for 30 minutes.
Heat the olive oil in a large nonstick skillet set over medium heat. Add the shallots, carrot, celery, mushrooms, and orzo.
Cook, stirring occasionally, until the orzo is lightly toasted, about 10 minutes. Add the garlic, thyme, salt and pepper, and cook for 30 seconds.
Once the rice has cooked for 30 minutes, stir in the orzo mixture. Cover the saucepan and cook until the liquid is absorbed, about 10 minutes.
Stir in the parsley. Serve.