Cook the Pasta: Get your large pot of salted water to a rolling boil. Add the penne and cook according to package directions until it’s al dente—tender but still with a slight bite. Just before you drain, scoop out about a cup of the starchy pasta water and set it aside. Drain the pasta and set it aside.
Season and Sear the Chicken: While the pasta is cooking, pat your chicken breasts dry with a paper towel. Season them generously on both sides with your Cajun seasoning. Heat the butter and olive oil in your large skillet over medium-high heat. Carefully place the chicken in the hot pan. Sear for 5-7 minutes per side, only flipping once, until a deep golden-brown crust forms and the chicken is cooked through to 165°F (74°C). Transfer the cooked chicken to a cutting board and let it rest.
Start the Sauce: Reduce the heat to medium. In the same skillet, melt the remaining 2 tablespoons of butter. Sizzle the minced garlic for about 30-60 seconds until aromatic, but not browned.
Build the Foolproof Roux: Sprinkle the flour over the garlic butter and start whisking immediately. Continue to whisk for about 60 seconds. It will form a thick, golden paste. This is the foundation for a perfectly creamy sauce.
Deglaze and Create the Cream Sauce: While still whisking, slowly pour in the chicken broth. Use your whisk to scrape up any flavorful browned bits from the bottom of the pan. Once the broth is incorporated and smooth, slowly pour in the heavy cream, whisking continuously.
Thicken and Season: Bring the sauce to a gentle simmer. Stir in the Parmesan cheese until it melts completely. Let the sauce bubble gently, stirring occasionally, for 3-5 minutes, or until it has thickened enough to coat the back of a spoon. Season with salt and pepper to taste. If it's too thick, add a splash of reserved pasta water.
Combine and Serve: Slice your rested chicken into strips. Add the drained pasta and the sliced chicken to the skillet with the sauce. Toss everything together until the chicken is heated through and every piece of pasta is coated. Garnish with diced tomatoes and fresh parsley, and serve immediately.