How to Make It
Put the fried tofu pieces in a large heatproof bowl and pour boiling water over them to cover; drain immediately. When cool enough to handle, squeeze out the water. Cut the rectangles in half crosswise, making 24 almost-square pieces, each with one side that opens to form a pocket.
In a large nonreactive saucepan, combine the stock with the mirin, soy sauce and sugar and bring to a boil over high heat. Add the tofu squares and stir to moisten. Cover with a lid that will keep the tofu submerged and simmer gently over low heat for 15 minutes. Transfer to a plate and let cool. Before using, gently squeeze the tofu to release any liquid and pat dry with paper towels.
In a small skillet, toast the sesame seeds over moderate heat, stirring, until fragrant, about 3 minutes. Let cool on a plate.
Shape about 3 tablespoons of the Sushi Rice into a flattened oval. Slide it into a tofu pocket to just fill it. Repeat with remaining rice and tofu. Cover with a damp cloth until ready to eat. Serve the sushi with a generous pile of pickled ginger and a small bowl of the toasted sesame seeds for dipping.