Heat the broth in a medium saucepan; keep warm over low heat.

Melt 3 tablespoons of the butter in a large skillet over medium heat. When the butter begins to foam, add the onions and cook, stirring, until pale yellow and soft, about 5 minutes. Add the rice and stir quickly for a minute of two, until the rice is translucent and well coated with the butter. Add the prosciutto and stir for about 1 minute. Add about 1/2 cup of the hot broth and cook until it has been almost completely absorbed. Continue cooking and stirring the rice in this manner, adding broth 1/2 cup at a time, until the rice is tender but still firm to the bite, about 18 minutes.

When almost all of the last addition of broth is incorporated, add the remaining 1 tablespoon butter and about half of the Parmigiano. Stir quickly until the butter and cheese are melted and the rice has a moist, creamy consistency.

Taste, adjust seasoning, and serve immediately with the remaining Parmigiano.