Heat olive oil in a large pot or Dutch oven over medium heat. Add onion and cook until softened, about 5 minutes.
Add garlic and cook for 1 minute more.
Add mushrooms and cook until browned, about 8-10 minutes.
Pour in vegetable broth and add wild rice, thyme, salt, and pepper. Bring to a boil, then reduce heat and simmer for 45 minutes, or until rice is tender.
Stir in heavy cream and heat through. Do not boil.