Set the Instant Pot to 'Sauté' mode. Add sesame oil and let it heat up. Add minced ginger and garlic, stirring for about 30 seconds until fragrant.
Add chicken thighs to the pot and brown them on both sides for about 3-4 minutes.
Pour in the teriyaki sauce, soy sauce, and honey. Stir well to coat the chicken.
Rinse the jasmine rice under cold water until the water runs clear. Add the rinsed rice and chicken broth into the pot, stirring gently to combine. Make sure the rice is submerged.
Seal the Instant Pot lid and set it to 'Manual' mode on high pressure for 10 minutes.
When cooking is complete, allow for a natural pressure release for 5 minutes, then quick release any remaining pressure.
Open the lid, add the broccoli florets on top, and close the lid again for an additional 5 minutes of heat to steam the broccoli with the residual heat.
Fluff the rice with a fork, mixing in the broccoli. Taste and adjust seasoning as needed.
Spoon the teriyaki chicken over the rice, garnishing with chopped green onions and a sprinkle of sesame seeds.
Notes
Feel free to adjust the amount of honey and sauces to taste.