Peel, seed, and chop the butternut squash into large chunks.
Heat the olive oil in a large pot over medium heat. Add the onion and salt and saute until just beginning to brown, 6-8 minutes.
To the onion, add the garlic, chopped sage, chopped rosemary, black pepper, nutmeg, and cinnamon. Stir, cooking until just fragrant, then add the chicken broth.
Bring the broth to a boil before carefully adding the squash chunks. Bring to a simmer, cover, and cook until the squash is fork-tender, about 25 minutes.
Let the soup cool slightly, then blend until smooth, either using an immersion blender in the pot, or in batches with a traditional blender. If the soup is too thick, add a little extra broth during blending.
Return the soup to the pot over low heat. Swirl in the heavy cream. Taste and add more salt if necessary.
In a separate small saute pan, heat ¼ cup olive oil over medium-high heat. When the oil shimmers, add whole sage leaves, being careful not to crowd the pan. Fry the leaves about 45 seconds per side, then remove to a paper towel-lined plate to drain. (The extra oil from frying the sage can be saved and used later)
Serve the soup, topping each bowl with an extra drizzle of heavy cream and a few crispy sage leaves, with warm bread on the side, for dipping.