Young fontina, a superb melting cheese, adds lushness and a little tang to the strata. And remember to put whole nutmeg on your shopping list; a bit of the freshly grated spice amplifies the other flavors.
Heat oil in a large saute pan over medium heat until shimmering. Add onion and 1/2 teaspoon salt, and saute until translucent, about 3 minutes. Fill pan with as much spinach as will fit; cook, stirring, adding remainder a handful at a time as space allows. When all the spinach is wilted, stir in pepper and nutmeg. Drain spinach in a sieve. When cool enough to handle, squeeze excess moisture from spinach by hand.
Butter a 3-quart baking dish. Place a third of the bread in a single layer in dish. Top with half the spinach mixture and a third of the cheeses. Repeat layering with a third of the bread, remaining spinach mixture, and a third of the cheeses, then top with remaining bread.
Whisk together 6 eggs, 2 cups milk, and remaining 1/2 teaspoon salt, and carefully pour over bread. Cover with parchment, and gently press down with hands until egg mixture soaks through top of bread. Cover parchment with foil, and refrigerate at least 8 hours and up to 2 days.
Preheat oven to 350 degrees. Meanwhile, remove strata from refrigerator, uncover, and let stand 30 minutes. Whisk together remaining 2 eggs and 2/3 cup milk, and pour over strata, gently pressing between layers of bread with a spoon or spatula to ensure that egg mixture seeps to bottom. Sprinkle with remaining cheeses. Bake until puffed and golden brown in places, 45 to 50 minutes. Let cool 15 minutes before serving.