For the salty-sweet sauce: In a large bowl, whisk together the soy sauce, vinegar, miso, ginger, garlic, honey, grapeseed oil, and sesame oil.
Position two oven racks, one in the center and one in the top slot of the oven, and preheat the oven to 400°F.
Cut the block of tofu crosswise into four 1-inch-thick slices. Place the tofu slices on several sheets of paper towel to drain off the excess liquid. Tear or cut the mushrooms into 2-inch pieces.
Arrange the tofu evenly spaced and in a single layer on a sheet pan. Place the mushrooms between the tofu slices on the pan. Pour the sauce over the tofu and mushrooms, tossing with your hands to coat. Drizzle everything with the olive oil.
Transfer the pan to the center rack and roast the tofu and mushrooms until the glaze is set and begins to brown in spots on the tofu, about 20 minutes. Move the baking sheet to the upper rack and turn the broiler to high. Broil until the glaze is set and slightly charred in spots, about 5 minutes. Remove from the oven and scatter the fresh herbs over the top.
Divide the spinach and rice among four bowls. Top with the glazed mushrooms and tofu and serve immediately.