Preheat the oven to 375°F (190°C) and lightly spray a 9x13-inch baking dish with cooking spray.
Cook the jumbo pasta shells in a large pot of boiling salted water according to package directions until al dente; drain and set aside to cool slightly.
Pour 1/2 cup of the spaghetti sauce into the bottom of the prepared baking dish and spread it evenly.
In a mixing bowl combine the cottage cheese, 1½ cups of the shredded mozzarella, grated Parmesan, pesto, and the large egg; stir until well mixed.
Stuff each cooked shell with the cheese–pesto mixture and place the filled shells in the baking dish on top of the sauce in a single layer.
Spread the remaining spaghetti sauce over the arranged shells, then sprinkle the remaining ½ cup shredded mozzarella on top.
Bake uncovered in the preheated oven for 30 to 35 minutes, until the cheese is melted and bubbly and the dish is heated through.
Remove from the oven and let rest a few minutes before serving.
