Arrange tofu slices into a square baking dish in a single layer.
Stir water, soy sauce, balsamic vinegar, brown sugar, ginger, garlic, and cornstarch together in a small saucepan; bring to a boil while stirring continually. Pour sesame oil into the boiling mixture while stirring to incorporate fully; remove from heat and pour over the tofu.
Marinate tofu for 15 minutes.
Heat a small skillet over medium heat. Cook sesame seeds in skillet until fragrant, about 5 minutes.
Bake tofu in preheated oven until it looks glazed, about 25 minutes. Garnish with sesame seeds and green onion.