Place the fried meatballs on a foil-lined baking sheet. Remove and drain on a paper towel-lined plate. In batches, fry the meatballs until dark brown, 1 to 2 minutes.
Heat over medium-high heat until a deep-fry thermometer reaches 350 degrees F. In a large heavy-bottomed saucepan, pour equal parts olive oil and vegetable oil to fill the pan halfway. Insert 1 cube smoked mozzarella into the center of each meatball and form the meat around it, enclosing the cheese. Add the beef and pork and, using a wooden spoon or clean hands, stir until combined. In a food processor, pulse the shallots, sun-dried tomatoes, basil, shredded mozzarella, parmesan, tomato paste, red pepper flakes, 1 1/2 teaspoons salt and 1/2 teaspoon pepper until blended. Dice the smoked mozzarella into 1/2-inch cubes.
