Bring a large pot of water to a boil, add 1 tablespoon of salt, and cook the pasta according to the package directions until al dente.
Reserve half a cup of pasta water, then drain the pasta, cover it, and keep it warm.
Flatten the chicken breasts until they are even in thickness, then season them all over with 1½ tablespoons of Cajun seasoning.
Heat 2 teaspoons of oil in a large non-reactive skillet over medium-high heat, add the chicken, and sear on both sides.
Reduce the heat to low and sauté until the chicken is cooked through and reaches 165°F on a thermometer.
Transfer the chicken to a cutting board, slice it into thin strips, and cover to keep warm.
In the same skillet over medium heat, sauté the butter and garlic for 30 to 60 seconds until fragrant, then add the diced tomatoes and sauté for another 2 minutes.
Stir in the heavy whipping cream, the remaining Cajun seasoning to taste, and the parmesan cheese, bringing everything to a simmer.
Add the sliced chicken and cooked pasta to the sauce, tossing until combined and heated through, thinning the sauce with the reserved warm pasta water if desired.
Serve with freshly grated parmesan and chopped parsley.