In a large bowl, mix the beef, green beans, eggs, bread crumbs, Parmesan, salt, and pepper with your hands until well mixed. Form into 9 baseball-sized meatballs and place in a single layer in a 13-by-9-by-2-inch baking dish.
Cover with foil and bake until browned and a meat thermometer inserted in the center registers 165ºF, about 35 minutes. Uncover, pour the sauce over the meatballs, and bake, uncovered, for 15 minutes longer. Transfer 3 meatballs to an airtight container and refrigerate for the Meatball Pizza.
Meanwhile, cook the linguine according to the package’s directions. Divide among serving dishes and top with the meatballs and sauce and Parmesan.
Tip: The meatballs can be refrigerated in an airtight container for up to 3 days or frozen for up to 1 month.