Preheat oven to 450 degrees. Split bread horizontally. Layer one side with mozzarella, ham, and spinach, beginning and ending with mozzarella, seasoning with salt and pepper as you go. Close sandwich. (Mozzarella being in direct contact with bread on both sides will hold sandwich together as cheese melts.)
Brush a large baking sheet with some of the oil. Place sandwich on sheet; brush top with remaining oil. Place another baking sheet on top (cover bottom of sheet with aluminum foil, if necessary), and press down very firmly.
Bake panini, pressing down top baking sheet once or twice during baking, until cheese has melted and sandwich is golden, 20 to 25 minutes. Cut into 4 pieces, and serve with