Heat the olive oil in a large pot over medium heat until shimmering. Add the diced onion and sauté until translucent and fragrant, about 5 minutes, listening for a gentle sizzle.
Add the minced garlic and thyme leaves to the pot, stirring constantly for about 30 seconds until the garlic is fragrant, but not browned.
Stir in the chopped wild mushrooms, cooking for about 8-10 minutes, until they release their earthy aroma and soften, and the mixture starts to turn golden.
Carefully pour in the vegetable broth, bringing the mixture to a gentle simmer. Let it cook uncovered for 15 minutes, allowing the flavors to meld and the mushrooms to become tender.
Use an immersion blender to puree the soup directly in the pot until completely smooth and velvety, or transfer carefully to a blender and blend until silky.
Return the pureed soup to a gentle simmer, then stir in the heavy cream. Cook for another 3-5 minutes to warm through, adjusting seasoning with salt and pepper to taste.
Once heated through and well seasoned, ladle the soup into bowls, garnish with extra thyme or fresh herbs if desired, and serve hot.