In a large bowl, combine the chicken pieces with 1 tablespoon of soy sauce and 1 tablespoon of cornstarch. Mix well and let marinate for 15-20 minutes.
Heat the vegetable oil in a large skillet or wok over medium-high heat. Add the marinated chicken and cook until browned and cooked through, about 6-8 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add the minced garlic, ginger, and sliced jalapeños. Sauté for 2-3 minutes until fragrant.
In a small bowl, whisk together the remaining soy sauce, honey, rice vinegar, and water. Pour this mixture into the skillet and bring to a simmer.
Return the cooked chicken to the skillet and stir to coat it in the sauce. Cook for an additional 2-3 minutes until the sauce thickens slightly.
Remove from heat and garnish with chopped green onions and sesame seeds if desired.