In a large pot, heat olive oil over medium. Sauté shallots until soft (3-4 mins). Add garlic and thyme; cook 1 minute.
Add mushrooms and a pinch of salt. Cook until golden (8-10 mins), stirring occasionally.
Pour in wine (or ¼ cup stock) to deglaze the pot, scraping up browned bits.
Add chestnuts and stock. Simmer for 15 mins. Discard thyme sprigs.
Blend until smooth. Stir in cream, then season with salt, pepper, and a pinch of nutmeg.
Serve hot, garnished with a drizzle of truffle oil, fresh thyme, or crispy mushrooms.