Heat oven to 400°F. Lightly oil a 9×13-inch baking dish. Bring a large pot of well-salted water to a boil for the shells.
Make the sauce: Warm the olive oil in a large sauté pan over medium heat. Add the diced onion and cook until translucent, about 3 minutes. Stir in the garlic and cook 30 seconds. Add the sun-dried tomatoes, marinara, chicken broth, oregano, and red pepper flakes. Simmer gently for 8–10 minutes to thicken slightly. Off the heat, stir in the heavy cream and 1/4 teaspoon kosher salt; taste and adjust seasoning as needed.
Cook the shells: Boil the jumbo shells until just al dente and flexible, 9–10 minutes. Drain, rinse briefly under cool water, and spread on a parchment-lined sheet so they don’t stick (a spoonful of the sauce tossed with the shells helps keep them separate).
Mix the filling: In a large bowl, combine the ricotta, chicken, goat cheese, Parmesan, egg, basil, spinach, lemon zest (if using), Italian seasoning, black pepper, and 3/4 teaspoon kosher salt. Stir until creamy and cohesive.
Assemble: Spoon about 1 cup of the sauce into the prepared baking dish. Fill each shell generously with the ricotta-chicken mixture (use a small spoon or piping bag) and arrange them open-side up in the dish. Pour the remaining sauce evenly over and around the shells. Cover tightly with foil.
Bake covered for 18–20 minutes. Remove the foil, sprinkle the mozzarella over the top, and bake another 8–10 minutes until the cheese is melted and the edges are bubbly. For golden spots, broil 1–3 minutes, watching closely. Rest 5 minutes before serving; garnish with fresh basil and extra Parmesan, if desired.