In a large heavy pan, heat the olive oil over medium heat. Add the onion and sauté until tender, 5 to 7 minutes. Add the mushrooms and stir well. Cook until the mushrooms are soft and tender, another 5 to 7 minutes.
Add the wine and deglaze the pan, scraping up any browned bits off the bottom of the pan. Add 1 thyme sprig and reduce the heat to low. Simmer, stirring often, until most of the liquid has cooked off, about 30 minutes.
Stir in the butter and cook for 2 minutes more. Season with salt., then transfer to a serving dish. Garnish with the leaves from the remaining sprig of thyme.