Wipe mushrooms clean with a damp paper towel. Cut the stems so that they are right below the cap.
In a large skillet, heat the oil over high heat, but not smoking. Add the mushrooms placing them cut side down. Do not move the mushrooms until they have caramelized on the bottom. (5 mins or more) If you toss them too soon, they will release their liquid and begin to steam. When the bottoms are caramelized, toss them and continue to cook for about 5 minutes.
Turn the heat down to low/med. Add the vegan butter and diced shallots. Cook and toss for 5 minutes, until beautifully browned.
Season with salt and add the garlic. Saute another 2 minutes, and add the thyme, lemon juice, and white wine. Cook to evaporate the liquid.