Prepare the teriyaki sauce: In a small saucepan, combine the soy sauce, mirin, 1/2 cup water, brown sugar, minced garlic, and grated ginger. Bring the mixture to a simmer over medium heat, stirring until the sugar dissolves.
Make the slurry: In a small bowl, whisk together the cornstarch and 3 tablespoons of cold water until smooth. Slowly whisk the slurry into the simmering sauce. Continue to cook, stirring constantly, until the sauce thickens significantly to a sticky glaze consistency, about 1 to 2 minutes. Remove from heat and set aside.
Cook the chicken: Heat the vegetable oil in a large skillet or wok over medium-high heat. Add the chicken pieces and cook until browned on all sides and cooked through, about 6 to 8 minutes.
Glaze the chicken: Pour about half of the prepared teriyaki sauce over the cooked chicken. Toss to coat the chicken thoroughly. Let it cook for 1 minute to allow the glaze to adhere and become very sticky. Remove the chicken from the skillet and set aside.
Cook the vegetables: Add the sesame oil to the same skillet. Add the mixed vegetables and stir-fry for 3 to 5 minutes until they are tender-crisp.
Assemble the bowls: Divide the cooked jasmine rice among four serving bowls. Top the rice with the glazed teriyaki chicken and the stir-fried vegetables.
Finish the dish: Drizzle the remaining teriyaki sauce over the chicken and vegetables. Garnish with sesame seeds and sliced green onions before serving.
Notes
For the stickiest glaze, ensure you let the cornstarch slurry cook long enough to fully activate and thicken the sauce.
You can substitute chicken thighs for breasts; thighs remain juicier during cooking.
If you prefer a milder flavor, reduce the amount of soy sauce slightly.