Bring a large pot of salted water to a boil. Add the jumbo shells (cook a few extra if desired) and cook for about half the package time plus 1 minute, about 5–6 minutes, until slightly underdone; they should still be firm. Drain and rinse under cold water to stop cooking, then separate shells onto parchment or a sheet to cool.
Preheat the oven to 350°F (175°C). Lightly grease a 9×13-inch (3-quart) baking dish and spread half of the marinara sauce evenly across the bottom.
In a large mixing bowl, whisk the beaten egg. Add the ricotta, chopped fresh basil (or dried basil), dried oregano, dried thyme, dried parsley, minced garlic, and about 1 teaspoon salt and 1/2 teaspoon black pepper (adjust to taste). Stir until smooth and combined.
Stir 2 cups of the shredded mozzarella and all the grated Parmesan into the ricotta mixture until evenly combined.
Transfer the cheese filling to a large resealable plastic bag or piping bag and snip approximately a 1-inch corner. Pipe about 2 tablespoons of filling into each shell.
Arrange the stuffed shells in the prepared baking dish, open side up, packed close together. Spoon the remaining marinara sauce over the shells to fully cover them.
Cover the dish with foil and bake for 30 minutes. Remove the foil, sprinkle the remaining 1 cup shredded mozzarella evenly over the shells, and bake uncovered 5–7 more minutes until the cheese is melted and bubbly.
Let the dish rest a few minutes, then serve warm topped with chopped fresh basil or parsley and additional cracked pepper if desired.