Bring a large pot of salted water to a boil and add the jumbo pasta shells. Cook shells for about half the time listed on the package plus 1 minute (about 5–6 minutes) so they are al dente. Drain, rinse under cold water to stop cooking, drain again, and spread shells in a single layer on parchment or a sheet pan to cool and prevent sticking.
Preheat the oven to 350°F (175°C).
In a large bowl, whisk the beaten egg, then add the ricotta and mix until smooth. Stir in chopped basil (or dried basil), dried oregano, dried thyme, dried parsley, minced garlic, and salt and pepper to taste (about 1 teaspoon salt and 1/2 teaspoon pepper is suggested).
Stir in 2 cups of the shredded mozzarella and all of the grated Parmesan until evenly combined.
Transfer the cheese filling to a large resealable plastic bag or piping bag and snip a corner to pipe, or use a spoon to fill each shell with about 2 tablespoons of the mixture.
Spread half of the marinara sauce evenly over the bottom of a 9x13-inch (3-quart) baking dish.
Place the stuffed shells in the baking dish, open side up, packed close together. Pour the remaining marinara sauce over the shells to cover them evenly.
Cover the dish with foil and bake for 30 minutes.
Remove the foil, sprinkle the remaining 1 cup shredded mozzarella over the shells, and return to the oven for 5–7 minutes more, until the cheese is melted and bubbly. Garnish with chopped fresh basil or parsley and serve warm.
