Drain the excess water from the tofu container. Use a tofu press to remove the extra water from the block. Press for 20 minutes. If you do not have a press, place two paper towels on the bottom and top of the tofu block. Put the block on a plate. Then place a heavy pan on top of the tofu. Add additional weight if needed. Press for 15-30 minutes. Change the paper towels halfway through.
Cut the tofu block into ½ inch cubes, and add to a bowl.
Top with corn starch, and gently toss with your hands until evenly coated. Do not use a metal spoon as this will break and crumble the tofu.
Add olive oil to a skillet over medium-high heat. Preheat the skillet for a few minutes then add the tofu. Cook on each side of the tofu until crisp and golden brown. About 3 minutes per side. Use chopsticks or tongs to flip the tofu cubes.
While tofu is cooking, whisk together the teriyaki sauce, ginger paste, garlic, and corn starch.
Once the tofu is crisped on all sides, add the sauce to the skillet. It will thicken quickly! Toss the tofu in the sauce so that it is coated on all sides. Remove from the heat as soon as the sauce thickens.
Transfer to a bowl, and top with sesame seeds and chopped scallions.