Heat the olive oil in a Dutch oven or large sauté pan over medium heat. When the oil is hot and shimmering, add the onion, garlic, and a pinch of salt, and cook until the onions are very soft and translucent, about 5 minutes.
Add the cinnamon and brown rice and cook, stirring constantly, for 2-3 minutes to toast the grains. Stir in the butternut squash cubes, then add the vegetable broth, thyme sprigs, and sage leaves, and bring to a boil. Immediately lower to a simmer, cover with a lid, and cook for 35 minutes until the rice is just tender, the butternut squash is soft, and most of the liquid has been absorbed. (You still want a little liquid in the pan to help create the creamy texture of the finished rice.)
Remove the thyme sprigs and sage leaves from the rice. Give the rice a good stir, breaking down some the butternut squash cubes. (Your rice should have a risotto-like consistency.)
Stir in the Parmesan and Fontina cheeses, then stir in the thyme leaves. Taste and season with salt as needed. Serve warm.