Preheat the oven to 400 degrees F. Toss the Brussels sprouts and butternut squash with the olive oil on a rimmed baking sheet; season with salt and pepper. Spread in an even layer. Bake until tender and browned, about 30 minutes.
Meanwhile, bring 4 cups water, the milk and 1/2 teaspoon salt to a simmer in a large saucepan over medium-high heat. Whisk in the polenta. Bring to a boil, then reduce the heat to low. Cook, stirring often, until creamy, about 6 minutes. Whisk in the pumpkin puree. Cook, whisking, until warmed through, about 4 minutes.
Remove from the heat and stir in the grated parmesan, butter and sage; season with salt. Top each serving with the roasted vegetables and shaved parmesan; drizzle with olive oil.