Combine 3 cups vegetable broth and rice in a large bowl and allow it to stand for 10 minutes, stirring occasionally. Drain the rice, keeping the broth mixture separately, and let stand for an additional 10 minutes.

Meanwhile, heat the olive oil in a saucepan over medium high heat. Add the sage and fry briefly, about 15 seconds. Add the onion and garlic, and cook until fragrant, about 2 minutes. Add the rice and toast with the onions for 2 more minutes. Add the butternut squash, previously strained liquid, salt, and black pepper to the pot and bring to a boil, reduce to a very low simmer. Cover pot and simmer until all the liquid has been absorbed, about 15-20 minutes, stirring 1-2 times.

Add the parmesan cheese, and remaining 1 cup of broth, stir until the cheese has fully melted. Serve immediately.