For the bolognese sauce: Heat the olive oil in a large pot over medium-high heat. Add the beef and sausage and cook until brown, 4 to 5 minutes, stirring with a wooden spoon to break up the pieces. Sprinkle with salt and pepper. Remove the meats from the pot and set aside. Set the pot back over the heat and add a little more olive oil. Add the carrots, celery and onions. Cook until browned, about 5 minutes. Return the meats to the pot and pour in the tomato sauce. Simmer until very thick, about 40 minutes.
For the arancini: Heat the olive oil in a large saucepan over medium-high heat. Add the onions and salt and saute until transparent, about 4 minutes. Add the rice and cook, stirring constantly, until the rice is opaque and fragrant, about 1 minute. Pour in the wine and cook, stirring, until absorbed. While continually stirring with a wooden spoon, begin adding the stock in 1/2-cup increments, allowing the liquid to become completely absorbed by the rice between additions. Cook until the rice is just tender and the risotto is creamy, about 20 minutes.
Add the Romano, sprinkle with salt and pepper and stir to combine well. Transfer to a mixing bowl, stir in 2 cups of the Bolognese sauce and cool completely. Refrigerate until thoroughly chilled.
For cooking the arancini: Stir 1 of the eggs into the chilled rice mixture. Divide the mixture into about 3-tablespoon portions using a small scoop or large spoon, and then form into rough ball shapes using your hands.
Press a hole into the center of each rice ball and stuff the center with a chunk of provolone. Press the opening closed and roll the ball between your hands until it is smooth. Refrigerate to allow the balls to set before coating and frying, at least 1 hour.
Heat 2 inches of vegetable oil in a large saucepan until a deep-fry thermometer registers 360 degrees F. Place the panko, flour and remaining 2 eggs in 3 separate bowls. Lightly beat the eggs using a fork. One by one, lightly dredge each arancini in the flour, rolling to coat completely, then the beaten egg mixture, then the panko, so that each ball is completely coated.
Fry the balls in batches, a few at a time, turning once during cooking so that they are evenly browned, 2 to 3 minutes. Transfer the balls to paper-towel-lined plates. Serve hot or warm, sprinkled with Romano.
This recipe was provided by a chef, restaurant or culinary professional and makes a large quantity. The Food Network Kitchens chefs have not tested this recipe, in the proportions indicated, and therefore, we cannot make any representation as to the results.