How to Make It
Bring the chicken stock to a simmer in a medium saucepan; keep warm.
Melt the butter in a medium saucepan. Add the shallots and cook over moderate heat, stirring occasionally, until softened, about 3 minutes. Add the rice and cook, stirring, for 4 minutes.
Add 1 cup of the stock to the pan and cook, stirring gently, until all the stock is absorbed. Add the remaining stock, 1/2 cup at a time, and cook, stirring gently, until the rice is al dente, about 25 minutes. Stir in the Parmesan, 2 teaspoons of salt and 1/4 teaspoon of pepper.
Transfer the risotto to a heatproof bowl and let cool for 10 minutes. Stir in the parsley and 1 egg. Press a piece of plastic wrap directly onto the rice and refrigerate the risotto for at least 4 hours or, preferably, overnight.
Line a baking sheet with wax paper. In a shallow bowl, beat the remaining 3 eggs. Put the flour and bread crumbs on separate plates. Season the bread crumbs with salt. Using moistened hands, form 1/4-cup portions of the rice into 2-inch balls. Tuck a piece of mozzarella and a pea in the center of each rice ball and seal any holes. Set the balls on the baking sheet.
Dredge the rice balls in the flour, tapping off any excess. Working with 1 at a time, dip each ball in the egg, then coat with bread crumbs, rolling and pressing it into a compact ball.
Heat 1/2 inch of vegetable oil in a large cast-iron skillet. When the oil is very hot, add all of the rice balls and cook over moderate heat, turning, until golden and crisp all over, about 8 minutes. Drain the balls on paper towels, then transfer to a large platter. Sprinkle the arancini lightly with salt and serve.