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.
When cooled, butter slices on one side with 2 tablespoons butter then set aside.
Heat 2 Tbsp. butter in medium nonstick skillet over medium heat.
Sauté shallots until fragrant and translucent, about 3 minutes.
Add spinach and salt and pepper to taste and cook, stirring occasionally, until spinach and shallots are 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″ square baking dish with remaining 1 tablespoon butter.
Arrange half the buttered bread slices, buttered-side up, in single layer in dish – you may need to cut them to fit.
Sprinkle half of spinach mixture, then 1/2 of the grated cheese evenly over bread slices.
Sprinkle remaining spinach mixture and 1/2 of the cheese over bread.
Whisk eggs in medium bowl until combined.
Whisk in reduced wine, half-n-half, 1 teaspoon salt, 1/2 tsp. nutmeg and pepper to taste.
Pour egg mixture evenly over bread layers.
Cover the strata surface flush with plastic wrap, and then weigh it down. (I used a couple of boxes of pasta – Cooks Illustrated.com suggests using two boxes of brown sugar). Then refrigerate the strata for at least 1 hour or up to overnight. (NOTE: weighing down the strata helps to create a more uniform texture during baking).
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.
Bake until both edges and center are puffed and edges have pulled away slightly from sides of dish, 50 to 55 minutes (or about 60 minutes for doubled recipe).
Cool on wire rack for 5 minutes before serving.