Cook wild rice in 2 cups of water for 45 minutes or until it fluffs up. Drain any remaining liquid left in the pot. Set aside.
In a large pot, melt butter. Add onions, carrot, and celery. Sauté till soften, about 3 minutes.
Pour in chicken stock. Bring to a boil. Add kabocha squash. Lower heat and allow soup to simmer for 15 minutes.
Turn off heat. Remove pot from stove onto a hot pad. Puree soup with an immersion blender until smooth.
Turn on heat and place pot back onto stove. When it comes back to a boil, add cooked wild rice, salt, and pepper. Allow soup to simmer for 5 minutes on medium low setting.
Stir in cream and allow it heat through but not boil.
Turn off heat and serve warm.