Preheat the oven to 425°F and line a baking sheet with parchment paper.
Press the tofu for at least 15 minutes, then cut into bite-sized cubes.
Toss the tofu with 1 tablespoon soy sauce and 1 tablespoon toasted sesame oil.
Coat with 2 tablespoons cornstarch, then drizzle with neutral oil and spread on the baking sheet.
Bake for 20 to 25 minutes, flipping halfway, until golden and crisp.
Simmer the sauce ingredients in a small saucepan, then stir in the cornstarch slurry and cook until glossy.
Toss the hot tofu with the sauce, then finish with sesame seeds and green onions.