Add butter, shredded carrot, cinnamon, ginger, paprika, and salt to a large soup pot or dutch oven. Cook over medium-low heat until the carrots are soft and fragrant, then turn the heat to low.
Pulse chicken broth and cilantro in a blender 2-3 times until the cilantro has become fine. Pour this mixture into the soup pot and stir to combine.
Add coconut milk, chopped chicken, cooked white rice, lime juice, and soy sauce to the pot. Stir everything together until well combined.
Simmer the soup on medium-low heat for 5–10 minutes until everything is warmed through.