8–10 (1/2-inch thick) slices supermarket French or Italian bread (6–7 ounces)
5 tablespoons unsalted butter, softened
4 medium shallots, minced (about 1/2 cup)
6 oz package frozen chopped spinach, thawed and squeezed dry
8 oz cremini mushrooms, sliced
Salt and ground black pepper
1/2 cup medium-dry white wine, such as Sauvignon Blanc
6 ounces Gruyère cheese, grated (about 11/2 cups)
6 large eggs
1 3/4 cups half-and-half
Adjust oven rack to middle position and heat oven to 225 degrees. Arrange bread in single layer on large baking sheet and bake until dry and crisp, about 40 minutes, turning slices over halfway through drying time. (Alternatively, leave slices out overnight to dry.) When cooled, butter slices on one side with 2 tablespoons butter; set aside.
Heat 1 tablespoon of butter in medium nonstick skillet over medium heat. When foaming subsides, add mushrooms and brown. Remove from pan. Heat (another) 1 tablespoon of butter and add shallots. Sauté shallots until fragrant and translucent, about 3 minutes; add mushrooms, spinach, and salt and pepper to taste and cook, stirring occasionally, until combined, about 2 minutes. Transfer to medium bowl; set aside. Add wine to skillet, increase heat to medium-high, and simmer until reduced to 1/4 cup, 2 to 3 minutes; set aside.
Butter 8-inch square baking dish with remaining 1 tablespoon butter; arrange half of buttered bread slices, buttered-side up, in single layer in dish. Sprinkle half of spinach mixture, then 1/2 cup grated cheese evenly over bread slices. Arrange remaining bread slices in single layer over cheese; sprinkle remaining spinach mixture and another 1/2 cup cheese evenly over bread. Whisk eggs in medium bowl until combined; whisk in reduced wine, half-and-half, 1 teaspoon salt, and pepper to taste. Pour egg mixture evenly over bread layers; cover surface flush with plastic wrap, weigh down (use two 1-pound boxes of brown or powdered sugar, laid side by side over the plastic-covered surface), and refrigerate for at least 1 hour or overnight.
Remove dish from refrigerator and let stand at room temperature 20 minutes. Meanwhile, adjust oven rack to middle position and heat oven to 325 degrees. Uncover strata and sprinkle remaining 1/2 cup cheese evenly over surface; bake until both edges and center are puffed and edges have pulled away slightly from sides of dish, 50 to 55 minutes. Cool on wire rack 5 minutes; serve.