In a small bowl, whisk together the soy sauce, brown sugar, minced garlic, minced ginger (or ground ginger), and sriracha if using.
In the same bowl, dissolve the cornstarch in 1 tablespoon water to make a slurry, then whisk the slurry into the sauce and set aside.
Heat a large high-sided skillet or wok over medium-high heat until hot.
Add the ground chicken to the hot pan and cook, breaking it apart with a spatula, until no longer pink and an internal temperature of 165°F is reached; remove the cooked chicken to a plate and set aside.
Add the sesame oil to the pan, then add the chopped red bell pepper, shredded carrots, broccoli florets, and chopped red onion; cook, stirring occasionally, for 4–6 minutes until vegetables are tender-crisp.
Return the cooked ground chicken to the pan, pour in the prepared stir-fry sauce, and toss everything to coat evenly.
Cook 1–2 minutes more, stirring, until the sauce thickens and coats the chicken and vegetables, then remove from heat.
Garnish with chopped green onion and sesame seeds, then serve.