Preheat oven to 400 degrees.
Brush squash with 1 tablespoon of olive oil and sprinkle with salt and pepper.
Place squash cut-side down in a shallow baking dish. Fill dish with approximately 1 inch of water to prevent burning.
Meanwhile, place kale, brussel sprouts, and sweet potatoes on a separate baking sheet. Drizzle with 1 tablespoon olive oil. Season generously with paprika, garlic powder, salt and pepper. Bake for 20-25 minutes until tender.
Remove vegetables from the oven and transfer to a mixing large bowl. Set aside.
Heat 1 tablespoon of olive oil in a skillet over medium heat. Add the mushrooms, shallots, salt and pepper. Sauté until the mushrooms and shallots are caramelized. Remove from the heat and add to bowl with roasted vegetables.
Add balsamic vinegar to vegetables and mix to combine.
Divide mixture among the roasted squash halves. Drizzle with additional balsamic vinegar.
Roast for 10-15 more minutes until vegetables are heated through and edges of squash have browned.