Rinse and soak the rice in cold water for about 1 hour, then drain thoroughly.
Prep the vegetables by chopping the carrot, celery, and mushrooms into small, even pieces.
In a medium pot, heat sesame oil over medium heat. Add the drained rice and stir gently for a few minutes, until it begins to look slightly translucent.
Add chicken broth and bring to a gentle boil. Simmer for 20–25 minutes, stirring occasionally to prevent sticking. Start on medium-low heat, reducing further as the liquid cooks down.
Mix in the chopped vegetables, cover the pot, and let simmer for another 10–15 minutes until the vegetables are tender. Adjust thickness by adding more broth or water, if needed.
Fold in the seasoned chicken during the final few minutes of cooking, reserving a bit for garnish if you like. Taste and season with additional salt and pepper if needed. Serve warm, topped with scallions and sesame seeds if using.