1. In a 5- to 6-quart pan over high heat, bring 3 quarts water to a boil. Add fettuccine and stir often for 10 minutes.
2. Meanwhile, cut prosciutto into 1/4-inch-wide strips and rub with your fingers to separate pieces.
3. In a 10- to 12-inch frying pan over high heat, stir cheese and milk until cheese is melted and sauce is smooth, about 3 minutes. Add prosciutto, stir, and keep warm over low heat.
4. After pasta has cooked 10 minutes, add spinach to pan and push down to immerse in water. Continue to cook until pasta is tender to bite, about 2 minutes longer. Pour into a colander and drain well. Return pasta and spinach to pan; add sauce. Mix well, lifting with 2 forks. Serve in wide bowls; add pepper to taste.