Rinse the wild rice under cold water and set it aside.
Heat the olive oil in a large pot over medium heat. Add the diced onion and cook for 4 minutes until it softens.
Stir in the minced garlic and cook for 1 minute. Add the sliced cremini mushrooms and cook for 5 minutes until they release their liquid.
Pour in the vegetable broth. Add the rinsed wild rice, thyme sprigs, salt, and black pepper. Bring the pot to a boil.
Reduce the heat to low, cover the pot, and simmer for 50 minutes until the wild rice is tender.
Remove the thyme sprigs. Stir in the chopped parsley and serve.