Cook the pasta shells in boiling water until they begin to soften, about eight minutes. Drain the shells and rinse them under cold water to stop the cooking process.
Spread a thin layer of the tomato sauce on the bottom of a baking dish. Stuff each shell with two meatballs. Arrange the stuffed shells in the baking dish. Continue until all of the shells have been filled. Pour the remaining pasta sauce over the shells and top with the mozzarella and Parmesan cheese. Cover the dish with aluminum foil.
Bake the pasta until the meatballs are heated through, about 15 minutes. Remove the foil and continue to bake until the cheese begins to brown, about five minutes.
Serve immediately topped with the parsley or store in the refrigerator for up to 3 days.