Prepare the mozzarella by cutting it into 16 small, even cubes and set them aside in the refrigerator so they stay firm.
In a large mixing bowl, add the ground beef, breadcrumbs, grated Parmesan cheese, egg, milk, minced garlic, dried oregano, dried basil, salt, and black pepper.
Use clean hands or a spoon to gently combine the meat mixture just until everything is evenly mixed, being careful not to overwork the meat.
Divide the meat mixture into 16 equal portions by shaping it into a rough log and cutting it into even pieces, or by using a tablespoon to scoop similar amounts.
Take one portion of the meat mixture in your hand, flatten it into a small disc, and place one cube of mozzarella cheese in the center.
Carefully wrap the meat around the mozzarella cube, sealing it completely so no cheese is exposed, then roll it into a smooth ball; repeat with the remaining meat and mozzarella cubes.
Heat the olive oil in a large skillet over medium heat until it is hot but not smoking.
Place the stuffed meatballs in the skillet in a single layer, leaving a little space between them so they brown properly.
Cook the meatballs for about 6 to 8 minutes, turning them gently every couple of minutes, until they are browned on most sides.
Reduce the heat to medium-low, pour the tomato sauce evenly over the meatballs, and gently move them so they are lightly coated in the sauce.
Cover the skillet with a lid and let the meatballs simmer in the tomato sauce for 15 to 18 minutes, or until they are cooked through and no longer pink in the center.
Remove the lid and simmer for an additional 2 to 3 minutes to slightly thicken the tomato sauce if desired.
Turn off the heat, sprinkle the chopped fresh parsley over the stuffed meatballs with mozzarella cheese, and let them rest for 2 minutes before serving.