Over medium-low heat, melt butter in oil. Add shallot and cook until soft, about 5 minutes. Raise heat to medium. Add mushrooms, salt, pepper. Cook covered until mushrooms release their liquid, 6 minutes.
Uncover, raise heat to high. Cook until liquid evaporated and mushrooms are brown, 5 minutes. Add thyme and wine. cook until skillet is almost dry, 1 minute. Serve hot.
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