Step 1

Cook pasta in salted water according to package directions until barely al dente, about 10 minutes (about 3 minutes less than package directions indicate). Drain and immediately transfer to a large rimmed baking sheet; spread in a single layer. Set pasta aside. Toss together Gruyère and Parmigiano-Reggiano in a medium bowl, and set aside.

Step 2

Preheat broiler to high with oven rack in middle of oven. Bring heavy cream and salt to a simmer in a large saucepan over high. Reduce heat to medium; stir in nutmeg, and simmer, stirring often, 2 minutes. Remove from heat. Stir in 4 1/4 cups of the cheese mixture, in small batches, stirring until cheese is melted after each addition. Stir in cooked pasta. Spoon pasta mixture into a 2 1/2-quart broiler-proof baking dish; top with remaining 1 cup cheese mixture.

Step 3

Broil in preheated oven until cheese is melted and golden brown, 3 to 5 minutes. Let stand 10 minutes before serving. Serve with thinly sliced prosciutto.