Heat olive oil in a large pot over medium heat. Add onion and garlic; sauté until softened, about 5 minutes.

Stir in the pumpkin puree, cumin, paprika, cayenne, nutmeg, salt, and pepper. Cook for 1–2 minutes.

Pour in the vegetable broth, stir well, and bring to a simmer. Cook for 10 minutes.

Use an immersion blender or transfer to a blender in batches to blend until smooth.

Return to the pot if needed, stir in coconut milk or heavy cream, and heat gently for 5 more minutes.

Serve hot, topped with fresh herbs or grilled cheese cubes if desired.