Drain the tofu on a wire rack for at least one hour.
Set the tofu on a few layers of paper towels and cut it into 9 cubes. Sprinkle them evenly on all sides with the salt.
Grate the ginger into a pan and then gather up the pulp and squeeze out as much juice as you can into the pan. Discard the pulp.
Add the grated garlic, mirin, soy sauce, and black pepper to the pan. Bring the mixture to a boil and continue boiling until the sauce just starts to thicken and it no longer smells like alcohol (about a minute after it comes to a full boil). Transfer the sauce to a bowl and set aside.
To fry the tofu, heat 2-inches of oil in a heavy-bottomed pot until it reaches 360 degrees F (180 C). Be sure to use a deep pot and don't fill it more than 1/2 way as the the moisture in the tofu will make the oil bubble a lot.
Pat the tofu dry on all sides with fresh paper towels and carefully lower the tofu into the hot oil using tongs.
Fry the tofu undisturbed for about 5-6 minutes or until you're able to pull the tofu away from the bottom of the pot without breaking it. Flip the tofu over and let it continue frying for another 5-6 minutes or until it's golden brown on all sides.
Transfer the hot tofu straight into the bowl with the sauce and sprinkle on the sesame seeds. Toss to coat the tofu with glaze and then transfer the tofu to a serving plate.
Garnish with more sesame seeds, black pepper, and chopped scallion greens.