Finely chop mushrooms in a food processor. Scrape mushrooms out into a clean, cotton towel. (Note: Do not use terry cloth, and choose an old towel as you will stain it.)  Twist towel around mushrooms and wring out as much liquid as you can over the sink. Heat a large (10-inch) non-stick skillet over a burner set between medium and medium-high. Add 1 tablespoon butter and swirl to melt and avoid burning. Add mushrooms, shallots, a pinch of salt, a pinch of black pepper, and thyme. Cook, stirring frequently, until mushrooms appear dry and are beginning to brown; about 5 minutes. Stir in remaining tablespoon of butter, and, when melted, Vineyard Creek Pinot Grigio. Cook, stirring frequently. Remove from heat and cool.