Prepare the Pasta: Bring a large pot of generously salted water (1-2 tablespoons salt) to a rolling boil. Add the penne pasta and cook according to package directions until al dente, about 8-10 minutes. Before draining, reserve 1 cup of pasta cooking water. Drain the pasta and toss with a drizzle of olive oil to prevent sticking. Set aside.
Prepare the Chicken: Pat the chicken breasts completely dry with paper towels. If they're uneven in thickness, use a meat mallet to pound them to an even ¾-inch thickness. Season both sides generously with salt and freshly cracked black pepper.
Cook the Chicken: Heat 1 tablespoon of olive oil in a large skillet over medium-high heat until shimmering. Carefully add the chicken breasts and cook undisturbed for 5-6 minutes until a golden-brown crust forms. Flip and cook for another 5-6 minutes until the internal temperature reaches 165°F. Remove chicken to a cutting board and let rest for 5 minutes before slicing into strips or bite-sized pieces.
Build the Flavor Base: In the same skillet (don't clean it—those browned bits are flavor!), reduce heat to medium. Add the remaining tablespoon of olive oil if needed. Add minced garlic and sauté for 30-60 seconds until fragrant and just turning golden. Be careful not to burn. Add the chopped sun-dried tomatoes and sauté for 2-3 minutes, stirring frequently, until softened and aromatic.
Deglaze and Create Sauce: Pour the chicken broth into the skillet, scraping up all the browned bits from the bottom with a wooden spoon. Let simmer for 2 minutes to reduce slightly. Reduce heat to low and pour in the heavy cream, stirring constantly. Let the mixture come to a gentle simmer (not a rolling boil) and cook for 3-4 minutes, stirring occasionally, until it begins to thicken slightly.
Add Cheese and Season: Gradually add the grated Parmesan cheese to the warm (not boiling) sauce, stirring constantly until completely melted and the sauce is smooth and cohesive. Taste and adjust seasoning with additional salt and pepper as needed. If using red pepper flakes, add them now.
Combine Pasta and Chicken: Add the drained pasta to the skillet with the creamy sauce. Toss thoroughly until every piece of pasta is beautifully coated. If the sauce seems too thick, add reserved pasta water a few tablespoons at a time until you reach the perfect consistency—the sauce should coat the pasta generously but not be gluey. Gently fold in the sliced chicken pieces, distributing them evenly throughout.
Finish and Serve: Let everything warm through together over low heat for 1-2 minutes, allowing the flavors to meld. Remove from heat and tear fresh basil leaves over the top. Toss gently one final time. Serve immediately in warm bowls with additional Parmesan cheese on the side and extra fresh basil for garnish.
