Heat the vegetable oil in a large deep skillet or wide pot over medium-high heat.
Add the chicken thigh pieces and cook for 4-5 minutes, stirring occasionally, until browned on all sides but not fully cooked through. Remove chicken from the pan and set aside.
In the same pan, add the sliced onion, minced garlic, and grated ginger. Cook for 2-3 minutes until the onion softens and becomes fragrant.
Add the rinsed rice to the pan and stir to coat the rice with the onion, garlic, and ginger mixture.
Pour in the chicken broth, soy sauce, mirin, and brown sugar. Stir well to combine.
Return the browned chicken pieces to the pan, nestling them into the rice mixture.
Bring the mixture to a boil, then reduce heat to low. Cover the pan with a tight-fitting lid and simmer for 15 minutes.
After 15 minutes, add the broccoli florets, sliced carrot, and thawed peas on top of the rice and chicken. Cover and cook for an additional 5 minutes until the vegetables are tender and the rice is cooked through.
In a small bowl, mix the cornstarch and water to create a slurry.
Remove the lid and stir the slurry into the pan. Cook uncovered for 2-3 minutes, stirring gently, until the sauce thickens.
Sprinkle the sliced green onions and toasted sesame seeds over the top before serving.