Rinse the sushi rice in a strainer until the water runs clear, then add it to the rice cooker with the water. Cook according to the rice cooker's instructions.
While the rice is cooking, mix together the rice vinegar, sugar, and salt in a small bowl until the sugar and salt are dissolved.
Once the rice is done, transfer it to a large mixing bowl and add the vinegar mixture. Use a rice paddle or spatula to gently mix the rice until it's coated in the vinegar mixture. Let it cool to room temperature.
Slice the tofu into small rectangles and sprinkle with cornstarch, salt, and pepper.
Heat the oil in a pan over medium-high heat and add the tofu. Cook until golden brown and crispy on both sides, then remove from the heat and set aside.
In a small bowl, mix together the sauce ingredients.
Once the rice has cooled, arrange the sliced vegetables, mushrooms, edamame, pickled ginger, and green onions on top.
Drizzle the sauce over the vegetables and tofu, then sprinkle with sesame seeds.
Serve in a large serving dish.