Preheat oven to 425F.
Cut tofu into 1-inch cubes and blot with paper towels. In a large bowl, whisk together soy sauce, vegetable oil, and cornstarch. Add tofu and toss gently until tofu is coated with the mixture. Spread on a baking sheet in one layer and bake until golden brown, about 25-30 minutes, tossing halfway through.
To make the teriyaki sauce, combine soy sauce, mirin, brown sugar, sesame oil, garlic, and ginger in a small saucepan and simmer over medium heat. Dissolve cornstarch in two tablespoons of water and whisk into the sauce, stirring occasionally, until mixture thickens.
Serve tofu cubes over rice topped with teriyaki sauce, green onions, and sesame seeds.