In a small bowl, whisk 2 tablespoons soy sauce, ginger, garlic, and sesame oil together.
Place the chicken strips in a resealable plastic bag and pour the marinade over the chicken. Seal the bag and massage lightly to coat the chicken. Stash in the fridge and marinate for 1 hour.
While the chicken is marinating, in a medium bowl, whisk the remaining 2 tablespoons soy sauce, chicken broth, cornstarch, honey, and sriracha, if using.
When you're ready to cook, heat both sides of the griddle to medium-high. Add the vegetable oil and spread to coat the surface of the griddle.
Add the chicken and its marinade to one side of the griddle and the onion, pepper, and asparagus to the other. Cook, stirring frequently, and adjusting the heat as needed until the vegetables are crisp tender and the chicken is cooked through, about 6 minutes.
Mix the cooked chicken and vegetables together on the griddle and pour the stir fry sauce over the mixture. Working quickly, use the side of your spatula to continually scrape the liquid back towards the mixture and stir everything together until the sauce thickens and coats everything evenly, 1 to 2 minutes.
Scoop into a serving bowl and serve immediately, topped with sesame seeds, if desired.