Rinse wild rice under cold water. Combine rice with 3 cups of vegetable broth in a saucepan, bring to a boil, then reduce heat and simmer covered for 45 minutes or until tender. Drain excess liquid.
Heat olive oil in a large Dutch oven over medium heat.
Add onion, carrots, and celery. Sauté for 8 minutes until vegetables are softened.
Add minced garlic, thyme, nutmeg, and smoked paprika. Cook for 60 seconds until fragrant.
Stir in the pumpkin puree and the remaining 2 cups of vegetable broth. Whisk until the base is smooth.
Bring the mixture to a simmer, then reduce heat to low and cover. Simmer for 15 minutes.
Incorporate the cooked wild rice and heavy cream into the pot.
Heat for an additional 5 minutes over low heat to reach serving temperature, ensuring the liquid does not reach a rolling boil.
Season with salt and black pepper to taste.
Garnish with chopped parsley and serve immediately.