While potatoes are still hot, push through a ricer into a large bowl. Using a wooden spoon, stir in eggs, one at a time, mixing well after each addition. Add about half of the flour; mix well. Stir in enough of the remaining 1/2 cup flour to make a soft, pliable dough. Divide dough in thirds.
On a lightly floured surface, roll one portion of dough at a time into a 1-inch-thick rope. Cut rope into 1/2-inch pieces. Using your thumb, make an indentation in the top of each piece. Place on a baking sheet; chill while preparing the sauce (up to 2 hours).
For sauce, in a medium saucepan heat cream over medium heat. Stir in peas, salt, and pepper. Simmer gently for 3 minutes. Stir in prosciutto and 1/4 cup cheese; simmer gently for 1 minute more. Stir in butter until melted. Remove from heat; cover and keep warm.
In the Dutch oven bring a large amount of salted water to a rapid boil. Add half of the gnocchi; cook for 10 to 15 seconds or until gnocchi start to float. Using a slotted spoon, transfer to a warm serving bowl. Repeat with the remaining gnocchi.
Pour sauce over gnocchi; gently stir to coat. If desired, sprinkle with additional cheese.