Heat the olive oil in a large pot or Dutch oven over medium heat.
Add the diced onion, carrots, and celery. Sauté for about 5-7 minutes until the vegetables are softened, stirring occasionally.
Stir in the minced garlic and cook for an additional 1-2 minutes until fragrant.
Add the pumpkin puree, wild rice, broth, thyme, cumin, salt, and pepper to the pot. Stir to combine all the ingredients.
Bring the mixture to a boil, then reduce the heat to low. Cover the pot and let it simmer for 30 minutes, or until the wild rice is tender.
Once the rice is cooked, stir in the coconut milk. If you prefer a creamier soup, use a blender or immersion blender to puree a portion of the soup for a smoother texture.
Taste and adjust seasoning if necessary. Simmer for an additional 5 minutes, then serve hot, garnished with fresh parsley or pumpkin seeds if desired.