Grease a 9x13-inch dish with spray or butter.
Whisk eggs, milk, salt, pepper, and oregano in a large bowl.
Spread bread evenly in dish.
Distribute dry spinach, garlic, feta, and mozzarella evenly over bread.
Pour eggs over filling; press gently to soak bread.
Cover with plastic; refrigerate at least 2 hours or overnight for best texture.
To freeze, cover tightly with plastic then foil; freeze up to 3 months and thaw refrigerated overnight before baking.
Heat oven to 350°F; remove plastic and cover with foil. Bake 30 minutes, then uncovered 15 minutes until golden and center set.
Rest 5 minutes before cutting.