In a small bowl, combine the milk and breadcrumbs. Let the mixture sit for 5 minutes.
In a large bowl, combine the breadcrumb mixture with the ground meat, garlic, parsley, egg, salt and pepper.
Using your hands, mix together the ingredients just until combined. (Do not overmix or the meatballs will be tough.)
Divide the meat mixture into eight portions and roll it into balls. Insert a piece of string cheese into the center of each meatball, pinching the meat mixture to seal the cheese inside. Repeat the stuffing process with the remaining meat mixture.
Add the olive oil to a large skillet set over medium-high heat. Once the oil is hot, brown the meatballs on all sides in batches. Transfer the meatballs to a plate and wipe the skillet clean.
Add the tomato sauce to the skillet. Return the meatballs to the skillet and toss to combine with the sauce. Cover the skillet and simmer the meatballs over low heat until cooked through, about 10 minutes.
Top the meatballs with grated Parmesan cheese and parsley then serve with crusty bread for dipping.