In a large mixing bowl, combine the ground meat with 1 cup (about 150g) of fresh bread crumbs, 1 egg, a very generous grating of cheese, the chopped parsley, and a big pinch each of pepper and salt.
Mix the ingredients thoroughly by hand. The mixture should be soft enough that it can be rolled into very smooth balls, but not wet and sticky. Add more breadcrumbs if the mixture is too wet, or another egg if it’s too firm and crumbly. When you have a texture you like, scoop up enough meat to roll a 2-inch ball between your palms. Set it aside on a plate and repeat until all of the mixture has been used up.
In a medium saucepan, add the tomatoes, water, garlic, olive oil, basil, and a generous pinch of salt. Bring to a simmer and cook for 10 minutes. At this point, you should be able to mash the whole tomatoes with a fork. Do so, then gently add the meatballs into the sauce.
Bring the sauce to a simmer again, partially cover the pot, and let the meatballs cook until the sauce has thickened to your liking—up to an hour. As they cook, occasionally swirl the pot to turn the meatballs (it's ok if they don't remain completely covered). When the sauce is nearing completion, be sure to taste it and add salt as necessary to taste.