Scoop the soft, roasted flesh of the acorn squash from its shell and set aside.
In a large Dutch oven or heavy-bottomed pot, warm the olive oil over medium heat. Add the diced onion, carrots, and minced garlic, then sprinkle in the salt, rosemary, black pepper, nutmeg, and ground ginger. Stir occasionally, allowing the vegetables to soften and the aromatics to release their full flavor, about 5 to 7 minutes.
Pour in the vegetable broth, followed by the roasted squash. Stir to combine and bring the mixture to a gentle simmer. Lower the heat and let the soup cook for 20 minutes, allowing the flavors to meld and the vegetables to become fully tender.
Using an immersion blender, puree the soup directly in the pot until smooth and velvety. If using a countertop blender, work in batches, transferring the soup carefully and blending until a creamy consistency is achieved. Serve warm.