Preheat the oven to 400 degrees F and line a rimmed baking sheet with parchment paper. Turn up four edges of a large piece of foil to make a rectangular baking tray (about 12 by 3 inches) for the spinach; set aside.
Halve the block of tofu 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. Lay the tofu slices on 2 paper towels, and blot dry with 2 more, gently squeezing out as much moisture as possible. Sprinkle the tofu evenly with 1/2 teaspoon salt and set aside.
Spread the squash slices in an even layer on one side of the baking sheet. In a small bowl, whisk together the honey and 1 tablespoon of olive oil and drizzle it evenly over the squash (heat in the microwave for a few seconds if mixture is not pourable). Sprinkle with the chili powder and 1/4 teaspoon salt, and toss to coat.
Put the cornstarch on a plate. Crack the egg into 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 evenly space the breaded tofu on the other side of the baking sheet, leaving an empty space in the center.
Roast until the squash begins to soften, about 10 minutes, then turn the squash pieces over. Continue roasting until the panko is crisp and lightly browned at the edges, and the squash is beginning to caramelize, about 15 minutes more.
Remove the pan from the oven and lay the prepared foil tray in the center. Spread the spinach onto the tray and toss with the sesame oil, 1 teaspoon salt, 1/4 teaspoon pepper and the sesame seeds.
Return the pan to the oven and cook until the spinach has warmed through, the squash is completely tender and caramelized in spots, and the tofu is lightly browned and crunchy, about 5 minutes more. Divide between two plates and serve with your favorite dipping sauce.
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