Heat butter and olive oil over medium heat in a deep, cast iron skillet. Add the shallots and sauté until translucent, about 3 minutes. Add the garlic and sauté until fragrant, about 2 minutes more.
Working in batches, add the mushrooms to the pan and sauté until thoroughly browned. Repeat until all of the mushrooms are amber in color but not cooked through.
Cram all of the mushrooms into the skillet, sprinkle with salt and add the wine. Using butcher's twine, gather the sprigs of thyme together to form a bundle. Add the thyme to the pot. Bring the wine to a boil and reduce the heat to low. Cover the pot and let simmer for 30 minutes.
Remove the cover and increase the heat to medium. Cook until the liquid in the pot is reduced by half, about five minutes.
Remove the pot from the heat, cover and set aside until ready to serve.