Preheat oven to 400 degrees. Cook pasta a few minutes less than package instructions suggest. Cut prosciutto into thin strips.
In a 9-by-13-inch baking dish, toss pasta with spinach, half of prosciutto, milk, ricotta, and garlic. Season with salt and pepper. Top with remaining prosciutto and Parmesan. Bake until golden, 30 to 40 minutes.