Butter a 9x12-inch (or similar) baking dish.
In a large nonstick skillet, melt 3 tablespoons butter over medium heat. Add the bread cubes and cook, stirring occasionally, until lightly toasted, about 5 minutes. Remove the bread cubes from the skillet and spread half in the prepared baking dish. Set the remaining half aside.
Place the skillet back on the heat. Raise heat to medium-high, and add half the spinach, 1 teaspoon salt, ½ teaspoon pepper, and the nutmeg. Cook, stirring occasionally, until it starts to wilt. Add more spinach, in handfuls, until all of it is in the pan. Cook until all the spinach has wilted. Layer half the spinach over the bread. Top with half the grated cheese. Layer on the remaining half of the bread, spinach, and cheese.
In a large mixing bowl, whisk the eggs. Add the milk, mustard, 1 teaspoon salt, and ½ teaspoon pepper. Mix well. Pour over the bread, spinach, and cheese. Press down on the bread to submerge it. Cover with foil and refrigerate overnight.
Take casserole out of refrigerator and let sit at room temperature for 30 minutes. Preheat the oven to 375 degrees.
Bake the casserole, covered with foil, for 25 minutes. Remove foil and bake for another 10-15 minutes or until the cheese is fully melted and the eggs are set.