In a large pot, heat the olive oil over medium heat. Add the diced onion and sauté until translucent, about 5 minutes.
Stir in the minced garlic and sliced morel mushrooms, cooking for an additional 3-4 minutes until the mushrooms are tender.
Add the rinsed wild rice to the pot and stir to combine with the onion and mushrooms.
Pour in the vegetable broth and bring the mixture to a boil. Reduce heat to low, cover, and simmer for about 45 minutes, or until the wild rice is tender.
Once the rice is cooked, stir in the heavy cream, dried thyme, salt, and black pepper. Allow the soup to heat through for another 5 minutes.
Serve hot, garnished with fresh parsley.