Begin by making the brine. Combine the water, brown sugar, garlic, ginger, salt and thyme in a large resealable bag and swirl to dissolve the sugar. Add chicken pieces and allow to brine for 1 to 2 hours in the refrigerator.
Preheat grill to low-medium heat.
Make teriyaki glaze: In a small saucepan, over medium heat, combine teriyaki sauce, honey, ginger, garlic, and 1 teaspoon of sesame oil, and simmer until rich and slightly reduced.
Remove chicken from brine and pat dry. Discard the brine. Add the chicken to a large mixing bowl, drizzle with the 1/4 cup toasted sesame oil and season with freshly ground black pepper. Toss to coat and cook on a low-medium grill for 17 to 20 minutes per side until cooked through. Baste with teriyaki glaze for the last 5 to 7 minutes of cooking. Serve garnish with scallion threads (finely sliced scallions cut on the bias soaked in ice cold water), and toasted sesame seeds.