Make it for Sunday brunch, eat it for lunch and dinner. You won't be mad about it.
In medium ovenproof skillet, melt butter over medium heat. Add mushrooms, shallot, and 1 tbsp. thyme. Cook, stirring occasionally, until mushrooms brown, about 8 minutes. Add eggs and 1/4 cup cheese; season. Bake at 425° until eggs are just set, about 15 minutes. Top with more cheese and thyme.