Pat tofu dry with towels and cut into 1-inch cubes.
Preheat your air-fryer to 400°F (200°C) for 3 minutes. Grease the inner rack and arrange tofu in one layer, slightly apart on top. Then, spray or grease the tofu with a thin layer of oil.
Air-fry tofu until golden brown, about 10 minutes with a shake in between if needed. Transfer tofu to a plate and air fry until all tofu is done.
Heat a non-stick skillet over medium heat with a tablespoon of oil. Sauté ginger slices until aromatic or a brown crust on the edge is seen.
Add the water, kombu dashi, soy sauce, and mirin, then stir to combine and bring to a boil. Taste test.
Add the tofu and cover the pan with a lid. Simmer tofu over medium-high heat until the sauce has reduced to almost half. Increase the cooking time if you prefer a less saucy dish.
Meanwhile, dissolve cornstarch with a tablespoon of water.
Uncover and slowly add the cornstarch slurry until it thickens to your desired consistency.
Finally, add a drizzle of sesame oil and fold in the scallions before serving. (For softer scallions, let it cook a little longer)
Serve hot with a bowl of rice.