Heat oil in a large saucepan over medium heat. Add lemongrass, ginger and garlic, and cook until slightly browned, about 3-4 minutes.
Add Kaffir lime leaves, cilantro stems, Kabocha squash, and red curry paste. Cook for 2-3 minutes until fragrant.
Add coconut milk and water. Bring to a boil, reduce to low and simmer, covered, for 15 minutes. Turn off heat and leave on stove for ½ hour to allow flavors to meld.
Transfer everything to a blender and blend until smooth.
Serve, garnished with cilantro and Kaffir lime leaves, if desired.
Lemongrass and Kaffir lime leaves add a citrusy fragrance to this soup.