Using a clean tea towel, firmly press the block of Extra Firm Tofu (20 ounce) to remove the excess moisture. Cut the tofu into 1/2-inch slices. Then cut in half (around 2-3 inches across).
To make the marinade, mix Soy Sauce (1/2 cup), Rice Vinegar (1/4 cup), Mirin (1/4 cup), and Sesame Oil (2 teaspoon) in a large zip-top bag.
Add the tofu slices, close the bag, and gently move the tofu around to coat. Allow to marinate for at least 30 minutes, periodically turning the bag to coat all sides if the tofu.
Remove the tofu from the marinade and remove the excess moisture by pressing each piece firmly between several paper towels.
To set up your dipping station, beat Egg (1) with 1 tablespoon of water in a bowl. In a separate bowl, add Panko Breadcrumbs (1/2 cup), White Sesame Seeds (1/4 cup), Black Sesame Seeds (1/4 cup), and stir to combine.
Working with one slice at a time, dip the tofu in the egg mixture, being sure to coat the entire piece.
Transfer the tofu to the panko-sesame mixture, turning and pressing to coat.
Transfer the sesame crusted slices to a large dish and momentarily set aside.
Over medium-high heat, add enough Vegetable Oil (to taste) to cover the bottom of a heavy-bottomed skillet. Once hot, add the tofu slices in batches. Cook 2-3 minutes (or until golden-brown) on the first side.
Gently turn the tofu slices and cook the other side for another 2-3 minutes, or until golden-brown.
Lift the tofu out of the skillet and allow them to cool on a plate lined with a few paper towels.
As the tofu is cooling, make the dipping sauce by combining Lime Juice (4 tablespoon), Fish Sauce (2 tablespoon), Mirin (2 teaspoon) and Scallion (2 tablespoon) in a small bowl.
Once cool enough to handle, slice each tofu piece into bite-sized pieces.
Garnish with finely sliced Scallion (2) and serve with the dipping sauce.