Prep the rice and veggies. Cook your rice or grains according to package directions.
Slice the bell pepper, chop the broccoli into bite-size pieces, shred the carrots, and thinly slice the green onions.
Make the sauce. In a bowl, whisk soy sauce, honey, chili garlic sauce, rice vinegar, and toasted sesame oil. Stir in minced garlic and grated ginger. For a thicker sauce, whisk cornstarch with 2 tablespoons water and add it to the mixture.
Marinate the chicken (quickly). Cut chicken into bite-size pieces.
Toss with 2–3 tablespoons of the sauce and let it sit for 10–15 minutes while you heat the pan. Reserve the rest of the sauce for cooking.
Stir-fry the veggies. Heat 1 tablespoon neutral oil in a large skillet or wok over medium-high heat. Add broccoli and a pinch of salt; cook 2–3 minutes.
Add bell pepper and carrots; cook 2 minutes more until crisp-tender. Remove to a bowl.
Sear the chicken. Add another drizzle of oil to the pan. Spread chicken in a single layer and let it sear 2–3 minutes before stirring.
Cook until golden and just cooked through, about 5–7 minutes total.
Sauce it up. Pour the remaining sauce into the pan with the chicken. Let it bubble and thicken for 1–2 minutes, stirring to coat. If it gets too thick, add a splash of water to loosen.
Bring it together. Return the veggies to the pan and toss with the chicken.
Add sliced green onions. Taste and adjust: more chili for heat, a drizzle of honey for sweetness, or a squeeze of lime for brightness.
Build the bowls. Spoon rice into bowls, top with the chicken and veggies, and finish with toasted sesame seeds, extra green onion, and cilantro. Serve with lime wedges.