Start by peeling and dicing the butternut squash into roughly 1-inch cubes. Chop the onion and mince the garlic cloves, setting them aside.
Heat the olive oil in a large pot or Dutch oven over medium heat. Add the chopped onion and sauté for about 5 minutes, stirring occasionally, until translucent and fragrant. Toss in the minced garlic and cook for another 1-2 minutes, being careful not to let it brown.
Add the diced butternut squash to the pot and stir to combine with the onions and garlic. Sprinkle in the nutmeg and cinnamon, stirring well to coat the squash evenly with the spices.
Pour in the vegetable broth, making sure the squash is mostly submerged. Bring the mixture to a boil, then reduce the heat to low and let it simmer gently for 25-30 minutes, or until the squash is fork-tender.
Once the squash is soft, remove the pot from the heat. Using an immersion blender, puree the soup directly in the pot until silky smooth. Alternatively, carefully transfer the soup in batches to a countertop blender and blend until creamy.
Return the pot to low heat and stir in the heavy cream. Taste and season with salt and pepper as needed. Warm the bisque through, but avoid boiling once the cream is added to preserve its richness.
Ladle the Butternut Squash Bisque into bowls and garnish with chopped fresh parsley. Serve it up with crusty bread or alongside a fresh salad for a complete meal.