Set the oven rack to the middle position and preheat the oven to 375 degrees Fahrenheit.
In a large pot, bring 4 quarts water to a boil. Add 1 tablespoon kosher salt, stir to dissolve. Add in 1 pound spaghetti, cook according to package directions until al dente, about 10 minutes. Drain the noodles in a colander and rinse with cool water for about 30 seconds to stop the cooking.
Heat 2 tablespoons olive oil in a large skillet or dutch oven over medium-low heat. Add ½ cup finely chopped yellow onion, 1 tablespoon minced garlic, and 1 teaspoon Italian seasoning. Sauté until onions are translucent, about 3 minutes.
Add 2 cups marinara sauce, stir to combine. Cook until the sauce is hot, about 2 to 3 minutes. Turn off the heat and stir in ½ cup heavy cream. Season the sauce with more salt and pepper to taste.
Add the drained spaghetti to the sauce, stir to combine. Add 2 cups cooked shredded chicken and mix. Transfer the pasta to a 9 x 13-inch baking dish.
Sprinkle the pasta with 1 ½ cups shredded mozzarella cheese and ½ cup shredded parmesan cheese.
Cover with foil and bake until the cheese melts and the pasta is hot, about 15 to 20 minutes. For a more browned surface, remove the foil, and broil the casserole until lightly browned, about 2 to 5 minutes.
Garnish with 1 tablespoon chopped parsley, and serve immediately.