Combine the proscuitto and mozzarella in a bowl and set aside. (This will be the filling)
In a medium pot, heat the stock to a simmer.
Meanwhile, in a large heavy skillet or pot (preferably a Dutch oven), melt the butter over medium-high heat.
Add the shallots and cook until translucent, about 4 minutes.
Add the rice and cook until lightly toasted, about 8 minutes.
Add the wine and cook until almost evaporated, about 4 minutes.
Ladle over enough of the hot stock to cover the rice.
Stir frequently with a wooden spoon until almost all liquid is absorbed, about 8 minutes.
Add more stock and continue stirring until absorbed.
Add stock again, until absorbed and creamy and rice is soft (about 25 minutes total). Taste rice, if still not soft, continue adding hot stock and stirring until rice is soft and creamy. Don't let the risotto be too wet! Remove from the heat.
Add 3/4 teaspoon salt, Parmesan cheese and 2 eggs and gently mix to incorporate. Set aside and let cool completely.
Heat the oil over medium-high heat until it reaches 365°F.
Spread the flour on a plate and the bread crumbs in a separate plate.
Add the remaining eggs and 2 tablespoons of water in a medium bowl.
In another bowl, mix together prosciutto and mozzarella.
At this point, the risotto will be sticky. However, if the mixture is too wet to roll a ball, then gradually add in more parmesan cheese and bread crumbs until you can just form a ball. The balls will stay together after you dredge them. Wet hands (or lightly floured hands) help when dredging.
Scoop about 1/4 cup of the risotto (rice mixture) into the palm of your hand and place 1 portion of the prosciutto/mozzarella cheese mixture on top. Shape the rice into a ball and add more risotto, if necessary.
Roll the ball in flour, and then dip into the egg mixture to coat completely, shaking off excess.
Finally, roll the ball in the bread crumbs and place on a rack.
Repeat this process with remaining ingredients. Depending on the size of the rice balls, you wil have between 8 to 12 balls.
Using a slotted spoon, transfer the balls (a few at a time) to the hot oil and fry until golden, about 2 to 3 minutes.
Remove with slotted spoon and place on a rack. (Keep finished arancini in a warm oven).