Preheat the oven to 425 degrees F. Generously coat a rimmed baking sheet with cooking spray.
Remove the tofu from the packaging, and drain the excess water. Halve 1 of the blocks crosswise, halve each piece crosswise, then halve each piece again, for a total of 8 pieces 3 1/2 inches long by 1 3/4 inches wide by 1/2 inch thick. Repeat with the other block of tofu. Lay the pieces on 2 paper towels, and blot dry with 2 more, gently squeezing out as much moisture as possible. Sprinkle the tofu evenly with 1 teaspoon salt, and let stand.
Put the cornstarch on a plate. Crack the eggs in a shallow bowl, add 1 teaspoon salt and a few grinds of pepper and whisk until combined. Put the panko, 1 teaspoon salt and a few grinds of pepper in another shallow bowl. Line up the tofu, cornstarch, eggs, panko and the prepared baking sheet.
Working with 1 to 2 pieces of tofu at a time, coat them in the cornstarch, shaking off any excess, dip in the egg to coat, dredge in the panko, pressing the panko gently into the surface of the tofu, then transfer the breaded tofu to the baking sheet. Generously coat the tops of the tofu with cooking spray. Bake until browned and crisp, 30 to 35 minutes, turning the baking sheet halfway through.
Meanwhile, heat the vegetable oil in a small nonstick skillet over medium heat. Add the ginger and garlic, and cook, stirring constantly, until fragrant and light brown, about 1 minute. Reduce the heat to low, stir in the preserves, sesame oil, vinegar and chili sauce until combined and cook until heated through, about 1 minute. Season the dipping sauce with 1/2 teaspoon salt, transfer to a serving bowl and serve alongside the tofu.
Never leave a child unattended in the kitchen. Limit the child to tasks that are safe and age-appropriate.
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