Heat oven to 425°F. Melt butter in a medium saucepan over low heat. Stir in flour and cook until mixture bubbles, about 2 minutes. Whisk in milk; bring to a boil over medium-high heat. Add salt and pepper. Reduce heat to low and cook, stirring often, 5 minutes. Remove from heat and stir in half the cheese; set aside.
Lightly butter a 9 x 13-inch baking dish. Thoroughly mix spinach with sauce and spoon into dish in an even layer. (Gratin can be made ahead to this point and refrigerated up to 2 days.)
Mix remaining 1/2 cup cheese and crushed croutons. Sprinkle evenly over spinach. Bake until cheese melts, about 10 minutes.