This entrée can be put together a day ahead and refrigerated—just let it stand at room temperature 30 minutes before baking.
Preheat oven to 350F. Grease 2 12-oz. soufflé dishes or 1 9-inch glass pie plate. Heat oil in nonstick skillet over high heat, and add mushrooms. Sauté 5 minutes, or until browned. Add garlic and thyme, and cook 1 minute. Stir in sherry, and cook 1 minute more, or until liquid has evaporated. Season with salt and pepper, and transfer to bowl.
Return pan to high heat. Add spinach and 1 Tbs. water, and cook 1 minute, or until spinach wilts. Season with salt and pepper, and place in colander. Press out all liquid, and chop. Toss spinach and bread with mushrooms.
Whisk broth and egg in small bowl. Pour over bread mixture, and add cheese, stirring until bread has absorbed all liquid. Spoon into prepared baking dishes, and press down lightly. Bake 40 minutes, or until browned and bubbling. Let stand 10 minutes so strata will set, then serve.