Start by rinsing the wild rice thoroughly under cold running water, then set it aside to drain. Heat the olive oil in a large saucepan over medium heat until shimmering, and add the diced onion. Sauté for about 5 minutes, until the onion becomes translucent and fragrant.
Add the minced garlic and sliced woodland mushrooms to the onions, cooking for another 5-7 minutes. Stir gently as the mushrooms soften and release their earthy aroma, and the mixture begins to smell fragrant and appear slightly browned.
Pour in the vegetable broth, then stir in the rinsed wild rice, diced carrots, and diced celery. Bring the mixture to a gentle simmer over medium heat. Cover partially and cook for about 30 minutes, stirring occasionally, until the rice is tender and the soup adopts a slightly thickened consistency.
Stir in the chopped sage and dried thyme, tasting and seasoning the soup with salt and pepper as needed. Allow the flavors to meld over low heat for another 5 minutes, letting the herbs infuse the broth with aromatic depth.
Remove the soup from heat, and serve hot, a hearty bowl filled with chewy wild rice, tender vegetables, and earthy mushroom pieces in a fragrant, slightly thickened broth. Enjoy the rustic textures and layered flavors with a slice of crusty bread if desired.