Prepare Squash and Vegetables: Prepare the squash before you begin. Cut it in half from top to bottom and remove the seeds. Cut each half into two large chunks then slice the chunks into wedges. Slice the skin off each wedge and chop the wedges into cubes. Kabocha squash skin is edible so don't worry if you don't get every little bit of skin off. Prepare the onion, garlic, ginger and carrot as well so you're ready to go.
Heat Oil: Heat your choice of cooking oil or other liquid in a large pot or dutch oven over medium heat.
Add Aromatics: Add the garlic, ginger, onion and carrot and saute for 4-5 minutes until soft and fragrant.
Add Spices: Add the curry powder, cumin, coriander, cayenne or chili flakes, salt and pepper, stir well and cook for 2-3 minutes.
Add Squash and Broth: Stir in the cubed squash and broth. If needed, you can add additional broth after blending to adjust the consistency to your preference. Bring to a low boil then reduce the heat and simmer lightly, uncovered, for approximately 15 minutes until the squash is fork tender.
Blend Soup: Either use an immersion blender in the pot to puree the soup or carefully transfer it to a blender and process until smooth and creamy. Be sure to allow the steam to escape while blending if you're using a blender.
Add Final Seasonings: Return the soup to the pot if you used a blender and mix in the coconut milk, lime, soy sauce, miso paste and sugar, if using. Season with additional salt and pepper, if needed.
Serve: Serve right away with fresh naan, sesame seeds, fresh cilantro, pumpkin seeds, roasted chickpeas or anything else you enjoy with soup.