In a small bowl, whisk together the soy sauce, mirin, brown sugar, grated ginger, and minced garlic. In a separate tiny bowl, mix the cornstarch with 1 tablespoon of water to create a slurry. Set both aside.

Pat the chicken thighs dry and cut them into 1-inch pieces. Season lightly with salt and pepper. Heat vegetable oil in a large skillet or wok over medium-high heat. Add the chicken in a single layer and cook for 5-7 minutes, stirring occasionally, until golden brown and cooked through. Remove the chicken from the skillet and set it aside.

Add a bit more oil to the same skillet if needed. Add the broccoli florets and sliced carrots. Stir-fry for 4-5 minutes until crisp-tender.

Return the cooked chicken to the skillet with the vegetables. Pour the teriyaki sauce mixture over everything and bring to a simmer. Stir in the cornstarch slurry and cook for 1-2 minutes, stirring constantly, until the sauce thickens.

Turn off the heat and stir in the sesame oil. Serve immediately over rice or noodles, garnished with sesame seeds and sliced green onions.