In a saucepan over high heat; bring the broth to a boil. Stri in the rice, butter and salt. Cover, reduce the heat to low and cook until the liquid is absorbed and the rice is tender, 18 to 20 minutes.
Transfer the rice to a bowl and stir in the Parmigiano-Reggiano. Let cool slightly, then stir in the whole egg and egg yolk. Let cool completely.
Spread the flour on a dinner plate, and spread the bread crumbs on a seperate plate. In a shallow bowl, lightly beat the egg whites until blended.
In a small bowl, mix together the prosciutto and mozzarella, and then divide the mixture into 12 equal portions. Moisten your hands with water. Scoop up 1/4 cup of the rice mixture and place it in the cupped palm of your hand. Flatten out the mixture slightly and place 1 portion of the proscuitto-mozzarella mixture in the center. Mold the rice over the filling, adding a bit more rice if needed to cover it completely. Shape the rice into a ball. Roll the ball in the flour, and then in the egg whites to coat completely. Finally, roll the ball in the bread crumbs and place on a rack. Continue with the remaining ingreadients to make 12 balls total. Rinse your hands frequently to prevent the rice from sticking to them. Let the balls dray on the rack for at least 15 minutes before frying, or refrigerate the balls for up to 1 hour.
Position the rack in the middle of the oven and preheat to 200 degrees F. Line a large baking sheet with paper towels and set it next to the stove. Pour the olive oil to a dept of 3 inches into a deep, heavy fry pan and heat to 375 degrees F on a deep-frying thermometer. The oil must cover the balls by at least 1 inch so they will cook evenly and not burst.
Using a slotted spoon or wire skimmer, gently lower a few of the rice balls into the hot oil, being careful not to crowd the pan. Fry until golden brown and crisp all over, about 2 minutes. Using the slotted spoon, transfer the arancini to the prepared baking sheet and place in the oven to keep warm. Fry the remaining arancini the same way, allowing the oil to return to the original frying temperature before adding the next batch.
Arrange the arancini on a warmed platter and serve immediately, or hold in the warmed oven for up to 1 hour before serving.