Heat the oven to 375°F. Cook shells in a large pot of water with the tablespoon salt until 2 minutes short of the package time, then drain gently and spread apart on a plate.
Brown beef and onion in a skillet for 7 to 8 minutes until the meat reaches 160°F. Drain excess fat, stir in garlic for 30 seconds and transfer to a bowl to cool for 5 minutes.
Simmer tomatoes, basil, 1/2 teaspoon sauce salt and pepper in the skillet for 5 minutes. Spread 1 cup sauce in a 9-by-13-inch baking dish.
Mix cooled beef with ricotta, egg, Parmesan and remaining salt. Fill the shells evenly and arrange open-side up in the dish; spoon remaining sauce over and between them and scatter mozzarella on top.
Cover with foil and bake for 25 minutes. Uncover and bake for 8 to 10 minutes until bubbling and the filling reaches 165°F, then rest for 5 minutes and serve three shells per person.