Adjust oven rack to lowest position and heat oven to 500 degrees. Lightly brush mushroom caps with 2 tablespoons of oil, sprinkle with salt and pepper, and lay them, cap side up along the long side on a large (12- by 18-inch) rimmed baking sheet. Toss potatoes and onions with 1 tablespoon of oil and a sprinkling of salt and pepper. Add to baking sheet. Toss Brussels sprouts with 1 tablespoon of oil and a sprinkling of salt and pepper; set aside.
Mix remaining 3 tablespoons olive oil along with lime juice, thyme, oregano, cumin, and garlic powder in a small bowl; Drizzle about 3/4 of the seasoning over the mushrooms and potatoes. Toss remaining seasoning with Brussels sprouts.
Place baking sheet in oven and roast until mushrooms are impressively brown, about 20 minutes. Remove them from the baking sheet, stir the potatoes, and pour the Brussels sprouts on the empty space. Continue to roast until potatoes and onions are impressively brown and Brussels sprouts are tender-crisp (or to your taste), 10 to 12 minutes longer. Taste, adjust seasonings, and serve.