Preheat the oven to 350°F (175°C) and lightly grease a 9x13-inch baking dish.
In a large bowl, combine the shredded chicken, ricotta, lightly beaten egg, 1 cup of the mozzarella, 1/3 cup grated Parmesan, dried oregano, and salt and pepper; mix until evenly blended.
Transfer the mixture to a piping bag or a resealable plastic bag with a corner snipped off, then evenly fill each cooked manicotti shell without overfilling.
Arrange the stuffed shells in a single layer in the prepared baking dish.
In a small bowl, stir together the marinara sauce, 1/2 cup water, and Italian seasoning, then pour the sauce evenly over the arranged shells.
Sprinkle the remaining 3/4 cup mozzarella over the sauced shells and, if desired, a little extra Parmesan on top.
Bake for 35 to 40 minutes, until the sauce is bubbling and the cheese is melted and lightly browned.
Remove from the oven and let stand 5 minutes, then garnish with chopped fresh basil if using and serve.