Rinse the wild rice thoroughly under cold water using a fine-mesh sieve. This helps remove any dust or debris.
In a medium saucepan, combine the rinsed wild rice and vegetable broth. Bring to a boil, then reduce heat to low, cover, and simmer for 45-55 minutes, or until the rice is tender and has opened up. Drain any excess liquid.
While the rice is simmering, heat the olive oil in a separate skillet over medium heat. Add the chopped onion and cook until softened and translucent, about 5-7 minutes.
Add the minced garlic, sliced mushrooms, chopped celery, and chopped carrots to the skillet. Cook, stirring occasionally, until the vegetables are tender-crisp, about 8-10 minutes.
Stir in the dried thyme and cook for another minute until fragrant.
Once the wild rice is cooked and drained, add it to the skillet with the sautéed vegetables. Gently stir to combine.
Fold in the fresh parsley and chives (if using). Season generously with salt and freshly ground black pepper to taste.
Serve hot as a delicious side dish.