Cut the kabocha in half and scoop out the seeds and the hairy part on the inside. Chop the kabocha into pieces and slice off the green skin.
Add olive oil or butter to a large pot over medium high heat. Once hot, add the kabocha, carrots, and onion and sauté until onions start to turn translucent. Add in celery leaves and bay leaf and cook another minute until wilted. Add a splash of oil or broth if needed to prevent sticking to the pan.
Add vegetable broth and cashews (if using) and bring to a boil, then lower to simmer until the kabocha is soft, about 15 minutes. Check by inserting a skewer into the kabocha. When it pierces through easily, turn off the heat and remove the bay leaf.
Use an immersion blender to puree the soup until smooth. OR, if using cashews, transfer the soup to a high speed blender and blend until smooth. Add extra broth if the soup is too thick.
If using, stir in coconut milk, then add salt and pepper and adjust seasonings to taste. Gently reheat the soup if it's too cold (avoid boiling or the coconut milk may split). Serve warm.