Preheat the oven to 350°F (175°C).
Bring a large pot of lightly salted water to a boil, add the jumbo shells, and cook 8–10 minutes until al dente; drain and set aside to cool slightly.
In a large bowl, combine the beaten egg, ricotta, half of the mozzarella, half of the Parmesan, dried basil, salt, and black pepper; mix until well combined.
Spoon about half of the pasta sauce into the bottom of a 9×13 baking dish, spreading it into an even layer.
Stuff each cooked shell with the ricotta mixture and arrange the stuffed shells in the baking dish on top of the sauce (about 18–20 shells).
In a medium bowl, stir the remaining sauce together with the reserved mozzarella and Parmesan, then pour this cheese-sauce mixture evenly over the stuffed shells.
Bake in the preheated oven for about 30 minutes, until the edges are bubbly and the filling is set.
