In a heavy, small saucepan, bring the broth to boil. Remove from heat and cover.
In a heavy, medium saucepan, melt the butter over medium-low heat. Add the onion and sauté 4 minutes. Add the rice; stir 1 minute. Add the wine and stir until absorbed, about 1 minute. Add ½ cup of broth and simmer until the liquid is absorbed, stirring often. Cook until the rice is just tender and the risotto is creamy, adding the broth ½ cup at a time, stirring frequently and allowing each addition to be absorbed before adding the next, about 25 minutes.
Stir in the Parmesan. Season the risotto with salt and pepper.
Cool completely. Stir in the egg. Cover and chill.
PREPARE THE COATING and FILLING:
Place the flour in 1 bowl, and place the egg in another bowl. Place the breadcrumbs in a third bowl.
Using moistened hands, shape ¼ cup (packed) cold risotto into a ball. Poke a hole in the center. Fill with 1 rounded teaspoon of mozzarella and 1 teaspoon of prosciutto. Press the risotto over the filling. Coat the rice balls in flour, then egg, then breadcrumbs. Place on a rack to dry. Repeat with the remaining risotto, filling and coating. Let the rice balls stand at least 30 minutes and up to 1 hour.
COOK THE CROQUETTES:
Pour 1½ inches of oil into a heavy medium-sized pot. Attach a deep-fry thermometer and heat the oil to 360°F. Fry the risotto balls, 3 at a time, until golden and crusty, turning once, after about 2 minutes. Drain on paper towels.