Place 4 cups bread cubes in a single layer in a greased 13×9-in. baking dish. Sprinkle with 1 cup cheese and spinach. Layer with chorizo and onion; top with remaining bread and cheese.
In a large bowl, whisk eggs, milk, garlic salt and mustard. Pour over bread. Refrigerate, covered, several hours or overnight.
Preheat oven to 350°. Remove strata from refrigerator while oven heats. Bake, uncovered, until golden brown and a knife inserted near the center comes out clean, 40-45 minutes. Let stand 5-10 minutes before serving.