Place the tofu block between paper towels or a clean kitchen towel. Put a cutting board or a heavy object on top of the tofu to remove excess moisture. Let it press for about 15 minutes.
In a small bowl, whisk together soy sauce, mirin, brown sugar, and rice vinegar until the sugar dissolves. This is your teriyaki sauce.
Cut the pressed tofu into bite-sized cubes or rectangular pieces.
Place the tofu in a shallow dish or a Ziploc bag and pour the teriyaki sauce over it. Gently toss to coat the tofu evenly. Let it marinate for at least 15 minutes.
In a separate bowl, mix cornstarch with a little water to create a thick batter.
Heat vegetable oil in a frying pan or skillet over medium heat. Take each marinated tofu piece, dip it in the batter, and ensure it is fully coated. Shake off any excess batter.
Carefully place the coated tofu in the hot oil and fry until golden brown and crispy, turning occasionally to ensure even cooking. This process usually takes about 5-7 minutes.
Once the tofu is cooked, transfer it to a paper towel-lined plate or wire rack to drain any excess oil.
Garnish the Fried Teriyaki Tofu with sesame seeds and green onions if desired. Serve it hot as a main dish or a side dish with steamed rice or noodles.