Combine the chicken broth and basmati rice in a medium saucepan. Bring to a boil, then reduce heat, cover and simmer for 45 minutes (orzo mixture will be added in after 35 minutes - see next steps). ***Be sure the liquid continues simmer. If you have a gas stove, this likely can be achieved with low heat. Otherwise, turn up the heat slightly to maintain a simmer.
Heat the olive oil in a large nonstick skillet set over medium heat. Add the shallots, carrot, celery 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 35 minutes, stir in the orzo mixture. Cover the saucepan and cook until the liquid is absorbed, about 10 minutes.