Warm 1 tablespoon of neutral oil in a wide skillet (about 12 inches across) over medium-high heat until it begins to shimmer.
While the oil heats, pat dry 1½ pounds of boneless, skinless chicken thighs using paper towels. Evenly sprinkle with 1 teaspoon of kosher salt.
Arrange the chicken thighs in the skillet in one layer. Allow them to sear without moving until the underside is deeply golden brown, about 4 to 6 minutes.
As the chicken cooks, combine ⅓ cup mirin, ⅓ cup sake, ¼ cup soy sauce or tamari, ¼ cup water, and 2 tablespoons of packed brown sugar in a medium mixing bowl. Stir thoroughly until the sugar dissolves completely.
Scoop out 2 tablespoons of this sauce into a separate small bowl. Stir in 1 tablespoon of cornstarch until fully blended and no lumps remain.
Turn the chicken pieces over. Pour the remaining unsupplemented sauce into the pan. Let the liquid come to a boil, then reduce the heat to maintain an energetic simmer. Cook uncovered for another 5 to 10 minutes until the chicken is fully cooked through.
Lower the heat to medium. Using tongs, remove the chicken and transfer it to a clean cutting board. Re-stir the cornstarch mixture briefly to recombine. While whisking the pan sauce constantly, drizzle in the cornstarch blend. Continue whisking as the sauce thickens, about 30 seconds. Remove from heat.
Slice the chicken into ½-inch-wide strips and place them in a shallow dish or serving bowl. Pour the thickened glaze over the sliced meat. Top with finely sliced scallion and a sprinkle of sesame seeds if using.
Serve promptly with hot steamed rice and tender broccoli florets on the side.