Melt 1 tablespoon butter in large Dutch oven over medium heat. Cook half of prosciutto until lightly browned and crisp, about 5 minutes; transfer to paper towel-lined plate. Add spinach to pot in handfuls, stirring to allow each batch to wilt slightly before adding next. Transfer spinach to colander set over bowl and press with wooden spoon to release extra liquid.
Wipe out Dutch oven and melt remaining butter over medium heat. Add onion, remaining prosciutto and sage. Cook until onion is softened, about 5 minutes. Stir in garlic and nutmeg and cook until fragrant, about 30 seconds. Stir in flour and cook until golden, about 1 minute. Whisk in milk and simmer, stirring constantly, until thickened, about 3 minutes.
Return spinach to pot and stir until heated through, about 1 minute. Off heat, stir in 1/2 cup Parmesan and season with salt and pepper. Transfer to serving bowl, sprinkle with remaining Parmesan, and top with crispy prosciutto. Serve.