Preheat a large Dutch oven to medium-high heat with a drizzle of oil. Add the chicken in one layer and brown on both sides with a sprinkle of salt. You may need to do this in batches to not crowd the pan. Don't worry if the chicken isn't all the way cooked through, it'll finish cooking with the pasta.
Preheat the broiler. To the browned chicken, add the pasta, salt, marinara, and 4 cups of water. Stir well to lift any bits from the bottom of the pan, and reduce the heat to low.
Cover the pot and let the pasta simmer for 15 minutes total, stirring every 5 minutes to prevent sticking. The liquid should be bubbling but not boiling very aggressively. Turn the heat down if needed.
After 15 minutes, taste the pasta for doneness. The dish should be saucy but not soupy. If the pasta isn't done, add ½ cup more water, stir, and cover/cook for 2 minutes, repeating as needed until the pasta is cooked through. Add more salt during this time to taste.
When the pasta is cooked through, turn the heat off the stove. Stir ⅔ of the mozzarella cubes into the pasta.
Add the parmesan cheese and the rest of the mozzarella to the top of the chicken parmesan pasta. Broil the dish, uncovered, for about 3 minutes until the cheese is just starting to brown. Devour.