Make the katsu: Heat oven to 425 degrees. Grease 2 large rimmed baking sheets with the oil. Put cornstarch, eggs and bread crumbs in three separate shallow bowls, and add 3/4 teaspoon of the granulated onion to each bowl. Season all with salt and pepper and mix well. Add 3 tablespoons oil to the bread crumbs and mix well.

Working with one piece at a time, dust tofu in cornstarch, then dredge in egg, shaking off excess. Press in bread crumbs to evenly coat. Arrange on one baking sheet, and transfer to oven. Bake until golden and crisp, 15 minutes.

Place mushrooms on second baking sheet, season with salt and pepper and toss with the remaining 2 tablespoons oil. Bake until golden, 12 minutes.

Make the quinoa: Meanwhile, in a medium saucepan, combine quinoa with enough water to cover by 2 inches. Bring to a boil and cook until the quinoa is tender, about 8 minutes. Drain, then return quinoa to the pan. Cover and let stand for 10 minutes; fluff into a large bowl.

In a small bowl, combine tahini, oil, lemon juice, mustard, soy sauce, garlic and 1/2 cup plus 2 tablespoons of water. Whisk together and season with salt and pepper.

To the quinoa, add mushrooms, cauliflower, parsley and 1 cup of the dressing and mix well. Season with salt and pepper.

Divide quinoa in bowls and top with tofu. Serve with remaining sauce for drizzling on tofu and lemon wedges, if desired.