Preheat the oven to 475 degrees F. (See optional stovetop only directions below).
Heat oil in 12-inch oven-proof skillet over MEDIUM heat. Add the chicken. Cook and stir for a couple of minutes and then sprinkle chicken with 1/4 teaspoon salt, 1/4 teaspoon pepper, and 1/2 teaspoon each of thyme, rosemary, and oregano. Cook, stirring, until the chicken is just cooked through, about 8 to 10 minutes. Use a slotted spoon to transfer the chicken to a dish and set aside.
Add a bit more olive oil to the pan, if necessary, and return the pan to MEDIUM heat. Add the garlic and red pepper flakes. Cook and stir about 1 minute, until the garlic is fragrant, being careful not to allow it to burn. Add the marinara, chicken broth, water, and pasta to the pan, stirring to combine. Bring the mixture to a low boil, then cover the pan and reduce the heat slightly to keep it at a low simmer. Cook for 12 to 14 minutes, or until pasta is al dente.
When the pasta is tender, remove the cover and stir in 3/4 cup of the Parmesan cheese and the cooked chicken. Season to taste with additional salt and pepper, if desired. Remove the pan from the heat.
Sprinkle the top evenly with the mozzarella cheese and the remaining Parmesan cheese. Transfer the pan to the oven and bake for 5 minutes, or until the cheese has melted. If preferred you can complete this on the stove by covering the pan and keeping it over LOW heat until the cheese has melted.
Remove the pan from the oven (or stove) and sprinkle with fresh basil just before serving.