In a large mixing bowl, combine the cooled Arborio rice, eggs, Parmesan cheese, salt, and black pepper. Mix thoroughly until the ingredients are evenly incorporated and the rice mixture holds together when pressed.

Scoop about 2 tablespoons of the rice mixture into your hand and flatten it slightly. Place a small spoonful of Bolognese sauce and a cube of mozzarella in the center, then carefully wrap the rice around the filling and roll into a compact ball.

Place the flour, beaten eggs, and breadcrumbs into separate bowls. Roll each arancini first in flour, then dip into the beaten eggs, and finally coat completely with breadcrumbs for a crisp exterior.

Pour enough vegetable oil into a deep pan to allow the arancini to be submerged while frying. Heat the oil to 350°F (175°C) and maintain a steady temperature for even cooking.

Carefully lower a few arancini into the hot oil without overcrowding the pan. Fry for 3–4 minutes, turning occasionally, until they become deep golden brown and crispy on all sides.

Remove the cooked arancini using a slotted spoon and place them on paper towels to drain excess oil. Serve immediately while hot and crispy, accompanied by extra Bolognese sauce or marinara sauce for dipping.