Heat oven to 350°F and spray a 9x13 (3 qt.) baking dish with nonstick spray; set aside.
After cooking the pasta shells, drain and place them (separatelupside-down on a large sheet pan to dry.
Brown the beef, in a large skillet, set over medium heat until cooked through and no pink remains. Drain off the rendered fat.
Reduce heat to medium-low. Heat the olive oil, in the same skillet, and add the onion. Cook until translucent, about 3 minutes. Add the garlic and cook 30 seconds more.
Reduce heat to low and add the marinara; simmer uncovered, stirring occasionally, for 30 minutes.
In a medium bowl, mix together egg, cottage cheese, 1-cup mozzarella and ½ cup Parmesan.
Pour 3/4ths of the meat sauce in the bottom of the prepared baking dish.
Stuff the shells with 1 rounded tablespoon of cheese mixture and arrange them on top of the meat sauce, open-side up. Spoon the remaining meat sauce in-between the shells but not directly on top of the shells.
Cover with aluminum foil and bake 30 minutes. Remove the foil and sprinkle the remaining mozzarella and Parmesan over the shells. Bake 5-7 minutes longer, or until the cheese is melted.
Serve with garlic bread and a delicious salad.