Start by whisking together soy sauce, sake, mirin, water, and brown sugar in a bowl. Then, transfer 2 tablespoons of the mix to a smaller bowl and stir in cornstarch until it dissolves completely. This mixture will be used later to thicken the sauce.
Heat oil in a skillet over medium-high heat until shimmering. While the pan heats up, pat the chicken thighs dry with paper towels and sprinkle them evenly with kosher salt. Place the chicken in the hot pan in a single layer and sear without moving for about 4-6 minutes until golden brown on one side.
Flip the chicken pieces to cook the other side. Pour the larger portion of the sauce into the pan, allowing it to sizzle and bubble. Adjust the heat to maintain a consistent simmer, and cook for another 5-10 minutes until the chicken is fully cooked.
Once cooked through, transfer the chicken to a cutting board. Stir the cornstarch mixture again and slowly pour it into the simmering sauce while stirring. Cook for about 30 seconds until the sauce becomes thick and shiny.
Slice the chicken thighs into even strips and return them to the pan with the sauce. Toss to coat the pieces in the thickened sauce. Transfer everything to a serving dish, garnish with thinly sliced scallions and sesame seeds if desired, and serve alongside rice and broccoli.