Start by heating a large pot of salted water until it boils. Cook the penne pasta until just shy of al dente according to the package, setting aside 2 cups of the cooking water before draining.
While the pasta cooks, place the chicken pieces in a bowl, drizzle with 1 tablespoon of olive oil, season with 1 tablespoon of Cajun seasoning, and toss well.
Heat a Dutch oven or large heavy pot over medium-high heat, then add the chicken in an even layer and sear without stirring for about 3 minutes until the bottoms are golden brown. Flip and cook another 3 to 5 minutes until fully cooked, then transfer chicken to a plate.
To the same pot, pour in the remaining tablespoon of olive oil. Add the chopped onion, sliced bell peppers, garlic, and the remaining Cajun seasoning amount. Sauté, stirring occasionally, until the onions turn translucent and the peppers soften but remain crisp, about 5 minutes.
Turn the heat down to medium-low and stir in the canned fire-roasted tomatoes with their juice, cream cheese cubes, and grated Parmesan. Stir constantly until the cream cheese has melted completely, about 1 minute.
Return the cooked chicken and any juices accumulated on the plate back into the pot. Pour in 1 cup of the reserved pasta water along with the vinegar, mixing everything evenly.
Add the drained pasta to the pot and toss constantly for about 1 minute until the sauce clings nicely to the noodles. If the sauce is too thick, add extra pasta water a tablespoon at a time until you reach desired consistency.
Season the dish to taste with kosher salt and freshly ground black pepper. Serve sprinkled with extra Parmesan and chopped parsley if you like.
