Preheat the oven: Set your oven to 425°F to prepare for roasting.
Prepare the pickled carrots: In a small mixing bowl, combine the grated carrot with rice vinegar and sugar. Stir well and let the mixture sit for at least 10 minutes, or up to an hour, to allow the flavors to meld and lightly pickle the carrots.
Roast the Brussels sprouts: Toss the halved Brussels sprouts in a large bowl with the toasted sesame oil, 1 teaspoon of the peanut oil, Sriracha, and a sprinkle of salt and pepper. Spread them evenly on a baking sheet and roast in the oven until they are crispy and golden brown, about 30–35 minutes.
Prepare the mushrooms: In a separate bowl, toss the shiitake mushrooms with 1 tablespoon of peanut oil and season with salt and pepper. Arrange them in a single layer on another baking sheet. Add the mushrooms to the oven during the last 15 minutes of the Brussels sprouts' roasting time, cooking until they are deeply browned and tender.
Cook the tofu: Slice the tofu into ½-inch slabs, then cut the slabs diagonally into triangles. Heat about ¼ inch of peanut oil in a large nonstick skillet over medium-high heat. Fry the tofu in batches, cooking each side for 2–4 minutes until golden brown. Transfer the tofu pieces to a plate lined with paper towels and sprinkle with a pinch of salt while they are still hot.
Blend the miso dressing: In a blender, combine the grapeseed oil, toasted sesame oil, white miso paste, rice vinegar, ginger, garlic, lime zest, lime juice, honey, and 1 tablespoon of the pickled carrot mixture. Blend the ingredients until smooth and creamy, which should take 1–2 minutes.
Assemble the bowls: Divide the cooked grains evenly among four serving bowls. In a large bowl, toss the roasted Brussels sprouts and mushrooms together, then arrange them over the grains. Add a portion of the pickled carrots and fried tofu to each bowl. Garnish with fresh cilantro leaves, sesame seeds, and, if desired, slices of fresh red or green chile. Serve the miso dressing on the side for drizzling.