Prepare the pumpkin (if using fresh): Cut pumpkin in half, scoop out seeds, and roast cut-side down at 400°F for 30-40 minutes until tender. Scoop out flesh and set aside. Skip this step if using canned pumpkin.
Sauté the aromatics in a large pot over medium heat. Heat 2 tablespoons olive oil, add onion and cook until translucent, about 5 minutes. Add 2 minced garlic cloves and cook until fragrant, about 30 seconds.
Add pumpkin and seasonings to the pot. Stir in pumpkin puree, dried thyme, nutmeg, and cayenne (if using). Mix well to combine with the aromatics.
Pour in the broth and bring to a gentle simmer. Reduce heat to medium-low and let simmer for 15-20 minutes, allowing flavors to meld.
Blend the soup until completely smooth using an immersion blender directly in the pot. Alternatively, transfer in batches to a standard blender (being careful with the hot liquid).
Stir in the cream and return to low heat. Add salt and pepper to taste. Keep warm while preparing mushrooms.
Prepare the mushrooms by heating butter and 1 tablespoon olive oil in a separate sauté pan over medium-high heat. Add mushrooms in a single layer without overcrowding and let cook undisturbed for 2-3 minutes.
Season and finish mushrooms by stirring in remaining garlic and fresh thyme. Sauté until mushrooms are golden brown and garlic is fragrant, about 3-4 more minutes. Season with salt and pepper.
Serve the soup in warm bowls, topped with sautéed mushrooms and a sprinkle of toasted pumpkin seeds if desired.