Preheat to 425 F. Place two cups of cubed raw butternut squash on a rimmed baking sheet. Drizzle olive oil over top and season generously with salt and pepper. Toss to coat and arrange squash in a single layer on the baking sheet. Roast for 20-25 minutes, flipping halfway through, until squash can be pierced with a fork.
While the squash is roasting, prepare the other ingredients. Heat remaining olive oil in a medium-sized skillet over medium heat. Add the minced shallot and cook until softened, about 2-3 minutes. Add the kale and toss to coat. Season generously with salt and pepper. Add the vegetable broth and cook until wilted, about 5 minutes.
When you add the kale to the skillet, place 1 cup of oats and 2 cups of water in a large microwave safe bowl. Cover and cook for 5-6 minutes until water is absorbed. Let sit covered for 1 minute.
Stir oatmeal and divide between two bowls. Layer sautéed kale over top, followed by roasted butternut squash. Serve immediately.