Cook your brown or white rice according to the instructions (see below).
In a small bowl, whisk together the sauce ingredients until smooth. Set aside.
In a large skillet over medium-high heat, add 1 tablespoon oil. Once the oil is hot and shimmering, add half of the chicken pieces and cook, undisturbed, for 2-3 minutes, or until browned. Stir and cook for about 2 more minutes, or until cooked through. Transfer to a plate.
Add in the remaining 1 tablespoon oil and remaining chicken and repeat. Add the first batch of chicken back into the pan along with broccoli and cook for 1 minute, stirring often, to soften the broccoli a bit..
Add the teriyaki sauce and cook for 1 more minute, stirring constantly, or until the sauce thickens and coats everything nicely.
Serve with rice and top with scallions and sesame seeds.