Start cooking the rice according to package directions (about 15 minutes in a rice cooker for jasmine rice).
Mix cornstarch and cold water in a small bowl to make a slurry; set aside.
In a medium saucepan, combine soy sauce, mirin, grated ginger, chopped garlic, and honey. Bring to a gentle simmer over medium heat.
Stir in the cornstarch slurry and simmer 3–4 minutes until the sauce thickens enough to coat the back of a spoon. Remove from heat.
Slice chicken breasts into 1/2-inch strips and season with salt and pepper.
Heat avocado oil in a large skillet over medium-high heat. Cook chicken 5–6 minutes per side until no pink remains and internal temperature reaches 165°F.
While chicken cooks, steam broccoli florets and sliced bell peppers for about 5 minutes until tender-crisp.
Remove chicken from heat and toss with about 3/4 of the teriyaki sauce; reserve the remaining sauce for drizzling.
Portion cooked rice into the largest compartment of each meal prep container. Add chicken to a second compartment and vegetables to the third.
Drizzle remaining sauce over each portion. Cool containers with lids slightly open for 15 minutes to prevent condensation.
Seal containers and refrigerate. Pack sesame seeds and spring onions separately to add fresh when serving.