Whisk together the soy sauce, mirin, brown sugar, honey, rice vinegar, sesame oil, garlic, and ginger in a bowl until the sugar dissolves.
Reserve half the marinade in a small saucepan for the glaze and pour the remaining half into a zip-top bag with the chicken chunks.
Seal the bag and refrigerate for at least 1 hour, or up to 8 hours for deeper flavor.
If using wooden skewers, soak them in water for at least 30 minutes before grilling to prevent burning.
When ready to cook, preheat the grill to medium-high heat and brush the grates lightly with neutral oil.
Thread the marinated chicken chunks onto the skewers, leaving a small gap between pieces.
Bring the reserved marinade in the saucepan to a simmer over medium heat, add the cornstarch slurry, and stir for 1 to 2 minutes until the glaze thickens. Remove from heat and set aside.
Grill the skewers for 4 to 5 minutes per side, turning once, until the chicken is cooked through and the edges are deeply caramelized.
During the last minute of grilling, brush each skewer with the thickened glaze and turn once more to set it on the surface.
Transfer to a serving board, brush with any remaining glaze, and garnish with sesame seeds and sliced green onion before serving.