Heat vegetable oil in a large deep skillet or pot over medium-high heat.
Add the chicken thigh pieces and cook for 5-6 minutes, stirring occasionally, until browned on all sides but not fully cooked through.
Add the minced garlic and grated ginger to the pot and cook for 1 minute until fragrant.
Stir in the rinsed rice and cook for 1-2 minutes to lightly toast the rice.
In a small bowl, whisk together soy sauce, mirin, honey, rice vinegar, and water.
Pour the sauce mixture into the pot and stir to combine.
Bring the mixture to a boil, then reduce heat to low and cover the pot with a tight-fitting lid.
Simmer for 15 minutes without lifting the lid.
After 15 minutes, remove the lid and add broccoli florets and shredded carrots on top of the rice and chicken.
Cover again and cook for an additional 5 minutes until the vegetables are tender and the rice is fully cooked.
Remove from heat and let sit covered for 5 minutes.
Fluff the rice gently with a fork and stir to combine the vegetables and chicken evenly.
Garnish with sliced green onions and toasted sesame seeds before serving.