In a 5- to 6-quart pan, combine broth, milk, and fettuccine (break fettuccine if necessary to fit into pan); cover and bring to a boil over high heat, stirring occasionally. Reduce heat to medium-high and cook, uncovered, stirring often to separate noodles, for 5 minutes. Add peas and stir occasionally until pasta is tender to bite, 2 to 4 minutes longer.
Meanwhile, separate prosciutto slices and cut crosswise into 1/4-inch-wide strips.
In a small bowl, mix cornstarch with 2 tablespoons water until smooth. Add to pasta mixture and stir until it boils and thickens. Add sour cream, parmesan cheese, nutmeg, and salt and pepper to taste; stir until well blended and heated through, about 1 minute. Stir in prosciutto. Spoon onto plates.