Cook the pasta according to the package directions.
Heat the olive oil in a skillet over medium-high heat. Add the chicken pieces in a single layer and sprinkle with salt and pepper. Allow to cook, without stirring, until golden, about 2 minutes. Stir the chicken around to brown it on all sides. Remove to a plate.
In the same skillet over medium-high heat, add the garlic and onions and stir immediately to start cooking. Cook until the onions are deep golden, stirring occasionally, 2 to 3 minutes.
Reduce the heat to low and pour in the marinara sauce, red pepper flakes and 1/2 cup water. Stir until the onions and garlic are mixed in, then add the chicken back to the skillet. Add the parsley and stir to combine. Bring to a simmer and cook, stirring occasionally, for 7 to 8 minutes.
Make sure the sauce is bubbly and very hot, then gently stir in the mozzarella. Let sit, undisturbed, until you can see that the mozzarella is very soft, 2 to 3 minutes.
Drain the pasta and pour it onto a platter. Drizzle with a little olive oil. Immediately sprinkle on the Parmesan shavings. Pour on the sauce, sprinkle with grated Parmesan and the chiffonade of basil and serve immediately!