First, mix the cornstarch and water in a bowl so it dissolves fully. Then in a medium saucepan, combine this slurry with the brown sugar, soy sauce, garlic, rice vinegar, ginger, honey, and sesame oil. Stir consistently and bring the mixture to a simmer over medium heat until it lightly thickens—just enough that it coats the back of your spoon. Once it’s glossy and slightly thick, remove from heat and cool completely (placing it in the fridge helps speed this).
When the sauce is cool, place your cubed chicken into a large ziplock bag or bowl. Pour in half of the teriyaki sauce and toss or shake to coat every piece. Seal and refrigerate at least 30 minutes (or up to a few hours). Reserve the other half of the sauce for basting later.
After marinade time, thread the chicken cubes onto your soaked skewers (leaving a bit of space between pieces). Preheat your grill (or grill pan) to medium. Lightly oil the grates, then cook the skewers, turning every 3–4 minutes to get even char. Aim for internal temperature ~165 °F (74 °C). In the last few rotations, brush the reserved sauce over the chicken to build that shiny glaze.
Once cooked through and beautifully caramelized, remove the skewers from the grill. Let them rest a minute or two. Sprinkle it with sesame seeds and chopped green onion before serving. The flavors will deepen slightly while resting.