In a small bowl, whisk together the 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 of avocado oil in a large skillet or wok over medium-high heat.
Add the chopped broccoli and sliced red and orange bell peppers; stir-fry for 2–3 minutes until crisp-tender, stirring frequently.
Remove the vegetables from the pan and set aside.
Add the remaining 1 tablespoon of avocado oil to the pan and increase heat to medium-high.
Add the cubed chicken in a single layer without overcrowding; brown the pieces 1–2 minutes per side until lightly golden and mostly cooked through.
Pour the prepared sauce over the browned chicken and bring to a gentle boil, then reduce heat to low and simmer 2–3 minutes to thicken and finish cooking the chicken.
Return the cooked vegetables to the pan and simmer together for 3–4 minutes until the sauce is glossy and everything is heated through; adjust seasoning to taste and serve.
