Preheat the oven to 350°F (175°C) and grease a 9x13-inch baking dish.
In a large bowl, combine the shredded chicken, ricotta, beaten egg, 1 cup of the mozzarella, 1/3 cup Parmesan, dried oregano, and salt and pepper; mix until well blended.
Transfer the filling to a piping bag or a resealable plastic bag with a corner snipped off and fill each cooked manicotti shell, taking care not to overfill.
Arrange the stuffed shells in a single layer in the prepared baking dish.
In a small bowl, stir together the marinara sauce, water, and Italian seasoning, then pour evenly over the arranged shells.
Sprinkle the remaining 3/4 cup mozzarella over the top and, if desired, a little extra Parmesan.
Bake for 35–40 minutes, until the sauce bubbles and the cheese is melted and lightly browned.
Remove from the oven and let stand 5 minutes before serving; garnish with chopped fresh basil if desired.