In a small bowl, whisk together soy sauce, honey, grated ginger, minced garlic, rice vinegar, sriracha (if using), Dijon mustard, and cornstarch until smooth; set the sauce aside.
Heat 1 tablespoon avocado oil in a large skillet or wok over medium-high heat.
Add the chopped broccoli and sliced red and orange bell peppers to the hot pan and stir-fry for 2–3 minutes until they are bright and just tender; remove the vegetables to a plate.
Add the remaining 1 tablespoon of avocado oil to the pan and increase heat to medium-high.
Place the cubed chicken in a single layer (do not overcrowd) and brown for 1–2 minutes per side until golden on the outside and mostly cooked through.
Pour the prepared sauce over the browned chicken and bring to a simmer; when it bubbles, reduce heat to low and cook 2–3 minutes to thicken the sauce and finish cooking the chicken.
Return the cooked vegetables to the pan, toss to coat, and simmer together for an additional 3–4 minutes until everything is cooked through and the sauce is glossy.
Serve immediately.