Bring a large pot of water to a boil and add 1 Tbsp salt. Cook the pasta according to the package instructions until al dente. Reserve 1/2 cup of pasta water, then drain, cover, and keep warm.
Pound the chicken breasts to an even thickness and season them evenly with 1 1/2 Tbsp Cajun seasoning.
In a large non-reactive skillet, heat 2 tsp olive oil over medium-high heat. Once hot, add the chicken and sear on both sides. Lower the heat to low and sauté until the chicken is cooked through and reaches an internal temperature of 165˚F. Transfer the chicken to a cutting board, slice it into thin strips, and cover to keep warm.
In the same skillet, over medium heat, melt the butter and sauté the garlic for 30-60 seconds, or until fragrant. Add the diced tomatoes and cook for another 2 minutes.
Stir in the heavy whipping cream, add the remaining Cajun seasoning to taste, and mix in the Parmesan cheese. Bring the mixture to a simmer. Taste and adjust seasoning if needed.
Add the sliced chicken and cooked pasta to the sauce, tossing to combine until the pasta and chicken are heated through. If desired, add the reserved pasta water to thin the sauce. Serve with freshly grated Parmesan and chopped parsley.
