With your hands, combine the beef, veal, and pork in a large bowl. Add the eggs, cheese, parsley, minced garlic, and salt and pepper to taste and blend the ingredients together. Add the bread crumbs and blend into the meat mixture. Slowly add the water, 1 cup at a time, until the mixture is moist.
Shape the meat mixture into 2 1/2 to 3-inch balls.
Heat the oil in a large skillet. Sauté the whole garlic until lightly brown to flavor the oil, about 1 to 2 minutes.
Remove the garlic with a slotted spoon and discard.
Add the meatballs and fry in batches, being careful not to crowd the pan. When the bottom half of the meatball is well browned and slightly crisp, about 5 to 6 minutes, turn it and cook the other side for 5 minutes more.
Remove the meatballs from the heat and drain them on paper towels.