Mix cornstarch and ¼ cup water together in a cup; stir until dissolved and set aside.

In a high-speed blender, add the remaining teriyaki sauce ingredients, including remaining water. Blend on medium-low speed until the mixture is well combined and there are no large chunks of ginger or garlic. This step should take about 45 seconds. Transfer the mixture to a medium saucepan, set it over medium heat and let the sauce come to a boil. Once it's boiling, reduce the heat to low and whisk the sauce for 5-7 minutes. Add cornstarch mixture to the saucepan. Cook, stirring continuously until sauce has thickened, 3-5 minutes.

Take the sauce off the heat and transfer it to a medium baking tin to let it cool.

Drain the tofu and wrap it in a paper towel. Place a heavy object on top, such as a cast-iron skillet, to press out any excess liquid. Set aside for at least 15 minutes. Cut the tofu into bite-sized (about ½-inch) pieces and transfer to the baking tin with teriyaki sauce. Cover all the pieces in sauce and marinate for at least 1 hour, tossing from time to time. Meanwhile, soak the wooden skewers in warm water.

Preheat a grill to medium-high heat. Remove the skewers from the water and pat dry. Thread the tofu onto skewers. Grill the skewers for 3-5 minutes on each side, until they are lightly charred. Brush the skewers with the remaining teriyaki glaze every now and then, turning to coat evenly. Serve the skewers hot, garnished with shredded chives and sesame seeds.