Preheat the oven to 425°F. Toss together the Brussels sprouts, carrots, onion, 1 tablespoon of the olive oil, 1/2 teaspoon of the salt, and 1/4 teaspoon of the black pepper in a bowl. Spread the mixture in an even layer on a rimmed baking sheet. Bake in preheated oven until the vegetables are tender and caramelized, about 25 minutes.
Remove and discard the skin from the chicken. Remove the meat, and shred to equal about 2 cups. Whisk together the preserved lemon, shallot, vinegar, coconut sugar, curry powder, and 2 tablespoons of the olive oil in a small bowl. Toss the shredded chicken with 3 tablespoons of the dressing.
Pulse the florets in a food processor until the cauliflower is finely chopped and resembles uncooked rice or couscous. Heat the remaining 1 tablespoon olive oil in a large nonstick skillet over medium-high; add the cauliflower and remaining 1/4 teaspoon each of salt and pepper, and cook, stirring once or twice, until just beginning to brown, about 8 minutes. Divide the cauliflower evenly among 4 bowls; top with the caramelized vegetables and chicken, and drizzle with the remaining dressing. Sprinkle with the cashews.