Brush mushrooms clean and trim bottoms of stems. Tear clusters into large chunks.
Heat two large heavy (not nonstick) frying pans over medium-high heat 2 minutes. Divide mushrooms between pans and season lightly with salt. Cook until starting to release liquid, about 7 minutes. If mushrooms are very dry, add a splash or two of water.
Add 1 1/2 tbsp. butter and 4 or 5 branches thyme to each pan. Cook mushrooms, turning occasionally, until nicely browned, about 5 minutes. Add another 1 1/2 tbsp. butter to each pan and cook until tender, 7 to 10 minutes.
Into each pan, swirl 2 tbsp. sherry, then 1 tbsp. butter and 1 1/2 tsp. each lemon juice and vinegar. Cook over high heat, stirring occasionally, until sauce is glossy and mushrooms are coated, 2 minutes. Stir in a few tbsp. water as needed to loosen sauce. Season to taste with salt and more vinegar. Remove thyme.
Pour mushrooms into a serving dish and top with chives.
Make ahead: Through step 3, up to 1 day, chilled airtight in 1 pan. To reheat, add a few tbsp. water and heat gently in pan.